Find the values of the trigonometric functions of theta from the information given. cot(theta) = 15, cos(theta) > 0 sin(theta) = cos(theta) = tan(theta) = csc(theta) = sec(theta) =
Answers
Given cot(theta) = 15 and cos(theta) > 0, we can find sin(theta), cos(theta), tan(theta), csc(theta), and sec(theta). We have sin(theta) = 1/√226, cos(theta) = 15/√226, tan(theta) = 1/15, csc(theta) = √226, and sec(theta) = √226/15.
First, we can use the fact that cot(theta) = cos(theta)/sin(theta) to find sin(theta) and cos(theta). Since cot(theta) = 15, we have:
cos(theta)/sin(theta) = 15
Multiplying both sides by sin(theta), we get:
cos(theta) = 15sin(theta)
Now, we can use the fact that cos(theta) > 0 to determine the sign of sin(theta). Since cos(theta) = 15sin(theta), we have:
15sin(theta) > 0
Dividing both sides by 15, we get:
sin(theta) > 0
So, we know that theta is in either the first or second quadrant.
Next, we can use the fact that sin(theta) = cos(theta) to find the values of sin(theta) and cos(theta). We have:
sin(theta) = cos(theta)
Using the Pythagorean identity, we know that:
sin^2(theta) + cos^2(theta) = 1
Substituting sin(theta) = cos(theta), we get:
2sin^2(theta) = 1
Solving for sin(theta), we get:
sin(theta) = 1/sqrt(2)
Since sin(theta) > 0, we know that theta is in the first quadrant.
Using the fact that sin(theta) = cos(theta), we also have:
cos(theta) = sin(theta) = 1/sqrt(2)
Now, we can find the remaining trigonometric functions. We have:
tan(theta) = sin(theta)/cos(theta) = (1/sqrt(2))/(1/sqrt(2)) = 1
csc(theta) = 1/sin(theta) = sqrt(2)
sec(theta) = 1/cos(theta) = sqrt(2)
Therefore, the values of the trigonometric functions of theta are:
sin(theta) = cos(theta) = 1/sqrt(2)
tan(theta) = 1
csc(theta) = sqrt(2)
sec(theta) = sqrt(2)
Given that cot(theta) = 15 and cos(theta) > 0, let's find the values of the trigonometric functions sin(theta), cos(theta), tan(theta), csc(theta), and sec(theta).
1. Since cot(theta) = 15, we can write it as cot(theta) = adjacent / opposite, where adjacent = 15 and opposite = 1 (since cotangent is the reciprocal of tangent). Using the Pythagorean theorem, we can find the hypotenuse:
hypotenuse = √(adjacent² + opposite²) = √(15² + 1²) = √226
2. Now we can find sin(theta) and cos(theta):
sin(theta) = opposite / hypotenuse = 1 / √226
cos(theta) = adjacent / hypotenuse = 15 / √226
3. To find tan(theta), we use the formula tan(theta) = sin(theta) / cos(theta):
tan(theta) = (1 / √226) / (15 / √226) = 1 / 15
4. Lastly, we can find the values of csc(theta) and sec(theta), which are the reciprocals of sin(theta) and cos(theta), respectively:
csc(theta) = √226 / 1 = √226
sec(theta) = √226 / 15
In summary:
sin(theta) = 1 / √226
cos(theta) = 15 / √226
tan(theta) = 1 / 15
csc(theta) = √226
sec(theta) = √226 / 15
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Related Questions
find the weight in kilograms of a 150 pound person
Answers
Answer:
The weight in kilograms of a 150 pound person is 68.039 kg
Step-by-step explanation:
Weight = 150 pounds.
We need to convert this to kg,
Now, 1 pound = 0.453592 kg.
Then, 150 pounds will be,
150 pounds = 150(0.453592) kg
So, 150 pounds = 68.039 kg
The weight of a 150 pound person is approximately 68.04 kilograms.
To convert the weight of a person from pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms.
Given that the person weighs 150 pounds, we can multiply this value by the conversion factor to find the weight in kilograms:
Weight in kilograms = 150 pounds * 0.4536 kilograms/pound
Weight in kilograms = 68.04 kilograms
Therefore, the weight of a 150 pound person is approximately 68.04 kilograms.
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This Question: 1 pt 9 of 14 (7 cc Find the area of the region bounded by the graph of f(x) = sin x and the x-axis on the interval (-2/3, 5x /6). The area is 0 (Type an exact answer, using radicals as needed.)
Answers
To find the area of the region bounded by the graph of f(x) = sin x and the x-axis on the interval (-2/3, 5x /6), we need to use the definite integral. We can use the formula:
∫[a, b] f(x) dx
where a is the lower bound of the interval and b is the upper bound of the interval. In this case, a = -2/3 and b = 5x /6. Therefore, we have:
∫[-2/3, 5x /6] sin x dx
We can evaluate this integral using the substitution u = cos x. This gives us:
∫[-2/3, 5x /6] sin x dx = -cos x |[-2/3, 5x /6] = -cos(5x/6) + cos(2/3)
Finally, we can substitute in the values for the upper and lower bounds of the interval to get the exact answer:
Area = -cos(5x/6) + cos(2/3) = 0
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(4.076 x 10^4) + (3.2 x 10^4)
Answers
Answer:
72760
Step-by-step explanation:
In the figure below is a regular polygon find the value of X (10x+4)
Answers
Answer:For the given figure the value of x is 14
Step-by-step explanation:
Given a regular polygon
A regular polygon is a polygon which has all sides equal and each side subtends equal interior angle at the center.
According to the figure
We are given a regular polygon with 10 sides
The angle subtended at the center is given as
(10x + 4)°
The Sum of interior angles = ( 10-2) = 1440°
So the angle subtended by one side at the center is given as follows
1440°/ 10 = 144°
Since the angle subtended at the center = 144° = (10x + 4)°
so by solving this we can get
140 = 10x
x = 14
Describe the difference between null vs alternative hypothesis
Answers
Statistical hypothesis testing employs the null and alternate hypotheses.
The alternative hypothesis of a test expresses the prediction of an effect or relationship based on your study, while the null hypothesis of the test does not yet predict an effect or an association between the variables.
A statement that there is no relationship between two variables is called a null hypothesis. Another hypothesis is that the two variables are statistically correlated.
Alternative unilateral (directional) or the bilateral (non-directional) hypotheses are also possible. Simple, complex, true, and false are the four main categories of null hypotheses. If the p-value is greater than the statistical significance level, null hypothesis is preferred.
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Assessment Analytics
Math
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G.16 Add, subtract, multiply, and divide fractions and mixed numbers: word problems KR7
Skill plans
Learn with an example ✓ or Watch a video >
Last week, Becky spent 1 1/2 hours watching television. Monica watched television for 1/2 as
many hours as Becky did. How many hours did Monica spend watching television?
Write your answer as a fraction or as a whole or mixed number.
Answers
Number of hours spent by Monica on TV is 45 minutes , the time spent by Becky is in mixed fraction.
What is mixed fraction?
A mixed fraction is one that has each its quotient and remainder delineated.
Main Body:
Number of hours spent by Becky on TV = 1 1/2 hours
This is a mixed fraction.
Converting into decimal form,
1 1/2 can be written as 1.5 hours
Converting hours into minutes ,
⇒1.5 * 60 = 90 minutes
Time spent by Monica = (1/2)* Becky's time
⇒Time spent by Monica = (1/2)*90
⇒ 45 minutes
Hence time spent by Monica is 45 minutes.
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Bill burns earnings are subject to deductions for Social Security, Medicare, and FIT. Today is cumulative earnings are $110,000. This week bill earns $1200 Bill who is married as paid weekly and claims three exemptions assume the Social Security rate is 6. 2% on $128,401. 45% for Medicare does not pay for the week is
Answers
Bill's earnings are subject to deductions for Social Security, Medicare, and Federal Income Tax (FIT). Today, Bill's cumulative earnings are $110,000. This week, Bill earned $1,200. As Bill is married, is paid weekly, and claims three exemptions, the Social Security rate is 6.2% of $128,401.45, and the Medicare rate is 1.45%. Bill will not pay FIT for the week.
To calculate Bill's earnings for the week, we first subtract the applicable deductions from his $1,200 gross earnings. The Social Security rate of 6.2% on $128,401.45 is $7,966.98, and the Medicare rate of 1.45% is $181.80. This means that $9,148.78 is deducted from Bill's $1,200 gross earnings, leaving him with a net earnings of $286.22.
To calculate Bill's total cumulative earnings, we need to add the $1,200 that he earned this week to his existing $110,000 cumulative earnings. Thus, Bill's total cumulative earnings are $111,200.
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8. What is the solution to 0,3(12x16)=0.4(12-3x)?
Answers
Answer: False
Step-by-step explanation: First, you are going to multiply the numbers in the first set of parenthesis, getting 72. Now, have 72 take the place of 12x6 in the equation. Your new equation looks like this: 0.3 x 72 = 0.4(12-3).
Going off of step one, you will be doing the same thing with the second set, but you will be subtracting instead. You will get 9, and plug it place of the parenthesis. Your equation now looks like o.3 x 72 = 0.4 x 9.
Next, you will multiply the set of numbers on the left side of the equal sign, getting 21.6. You now have an equation of 21.6 = 0.4 x 9.
Going off of step 3, you are going to do the exact same thing we did in step 3. Multiply 0.4 and 9, and you will get 3.6. The equation now looks like 21.6 = 3.6.
Now, the inequality is false because the left-hand side and right-hand side are two completely different numbers. A bigger number cannot be equal to a smaller number.
Hope this helps!
Find a vector function, r(t), that represents the curve of intersection of the two surfaces. the hyperbolic paraboloid z = x2 - y2 and the cylinder x2 + y2 = 9 = X = r(t)
Answers
The vector function that represents the curve of intersection is r(t) = <x, y, z> = <3cos(t), 3sin(t), 9cos(2t)>
Finding a vector function that represents the curve of intersectionFrom the question, we are to find a vector function, r(t) that represents the curve of intersection of the given two surfaces
To find a vector function that represents the curve of intersection between the hyperbolic paraboloid and the cylinder, we will parametrize the curve using the variable t.
Given the cylinder equation, x² + y² = 9,
Express x and y in terms of t
x = 3cos(t)
y = 3sin(t)
Substitute the expressions into the hyperbolic paraboloid equation, z = x² - y² and find z in terms of t
z = (3cos(t))² - (3sin(t))²
z = 9cos²(t) - 9sin(t)
z = 9(cos²(t) - sin²(t))
NOTE: cos²(x) - sin²(x) = cos(2x)
Thus,
z = 9cos(2t)
Hence, the vector function is r(t) = <x, y, z> = <3cos(t), 3sin(t), 9cos(2t)>
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radius is dash of the diameter
Answers
Answer:
Step-by-step explanation:
Radius is 1/2 of the diameter
or
Diameter is 2 of the radius
Is quadrilateral ABCD a parallelogram? Explain.
Answers
Answer:
don't know
Step-by-step explanation:
Angela, Emily, and Christina are on their school’s soccer team. The table below shows the number of shots each player made and missed.
Answers
The ratio of shots made to the shots missed for each player will be:
Angela = 4:1
Emily.= 3:1
Christina = 7:3
How to illustrate the ratio?It should be noted that from the information given, Angela made 12 shots and missed 3 shots. Therefore the ratio is:
= 12/3
= 4/1
= 4:1
Emily made 15 shots and missed 5 shots. Therefore the ratio is:
= 15/5
= 3/1
= 3:1
Christina made 21 shots and missed 9 shots. Therefore the ratio is:
= 21/9
= 7/3
= 7:3
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Geraldine is asked to explain the limits on the range of an exponential equation using the function f(x) = 2x. She makes these two statements: 1. As x increases infinitely, the y-values are continually doubled for each single increase in x. 2. As x decreases infinitely, the y-values are continually halved for each single decrease in x. She concludes that there are no limits within the set of real numbers on the range of this exponential function. Which best explains the accuracy of Geraldine's statements and her conclusion?
Answers
Answer:
"as x increases infinitely, the y-values are continually doubled for each single increase in x".
Step-by-step explanation:
Given the exponential equation f(x) = 2x of which Geraldine is asked to explain the limits on the range, the expression that best explains the accuracy of Geraldine's statements and her conclusion is that "as x increases infinitely, the y-values are continually doubled for each single increase in x".
for example let y = f(x) so thet y = 2x
for every va;ues of x, y will be doubled as shown;
If x = 1
y = 2(1) = 2
If x = 2
y = 2(2) = 4
If x = 3
y = 2(3) = 6
I can be seen that the value of y doubles for all values of x hence making her first statement accurate.
The second statement 'As x decreases infinitely, the y-values are continually halved for each single decrease in x'. is not totally right because the y values may not be halved for some values of x as x increases.
Her conclusion is not also right because there are limits within the set of real numbers on the range of this exponential function. for every value of x, y will always tend to a real value.
If algae grows at a rate that can be modeled by the exponential function A(t) = ae^rt, what is the surface area of algae on a pond if the initial area of the algae (a) is 2 square meters, the growth rate (r) is 10%, and the algae grows for three days (t)?
Answers
In this problem, we have a model for the growth of algae. The model is described in terms of the function:
\(A(t)=a\cdot e^{r\cdot t}.\)Where:
• A is the surface area of the algae,
,• t is the time in days,
,• a represents the initial area,
,• r is the growth rate.
From the statement, we know that:
• t = 3 days,
,• a = 2 m²,
,• r = 10% = 0.1.
Replacing these data in the formula above, we get:
\(A(3)=2m^2\cdot e^{0.1\cdot3}\cong2.7m^2.\)AnswerThe surface area after 3 days is approximately 2.7 m².
What is the probability that in a randomly selected composition of n has a second part and it is equal to 1
Answers
The probability of selecting a composition of n with a second part equal to 1 is equal to (n-1)/4.
Let us consider a composition of n as an ordered sequence of positive integers where the sum of the integers is n.
The number of compositions of n is equal to 2ⁿ⁻¹,
Since there are n-1 spaces between the numbers where we can choose to either include or exclude a separator.
To calculate the probability that a randomly selected composition of n has a second part equal to 1,
Consider the second part of the composition.
It can be any positive integer from 1 to n-1, inclusive.
For the second part to be equal to 1,
Choose 1 as the second number in the composition and distribute the remaining n-2 among the remaining slots.
There are n-1 slots left since the second slot is already occupied by the number 1.
The remaining n-2 can be distributed in 2ⁿ⁻³ ways, since there are n-3 spaces left to distribute the remaining numbers.
Therefore, the probability of selecting a composition of n with a second part equal to 1 is,
P = (n-1) × 2ⁿ⁻³ / 2ⁿ⁻¹
= ( n - 1 ) × 2ⁿ⁻³⁻ⁿ⁺¹
= ( n - 1 ) × 2⁻²
= (n-1) / 4
Therefore, the probability is equal to (n-1)/4.
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What is the value of x?
Answers
Answer:
46°
Step-by-step explanation:
from large triangle:
let the third unknown angle be 'a'
then,
a+x+7+85=180
a=88-x
now,from small triangle,
let the third unknown angle be 'b'
then,
b+x+2x=180
b=180-3x
b=a (vertically opposite angles)
then,
180-3x=88-x
2x=92
x=46
I NEED HELP can someone find the slope from these equations
Answers
y=mx+b with m being slope.
Answers 2, -1/2, and 2/3
Answer:
\( \underline{\boxed{if \: y = 2x + \frac{2}{3} \to \: the \: slope\to \boxed{m = 2} }}\\ \underline{\boxed{if \: y = - \frac{1}{2} x - 3 \to \: the \: slope\to \boxed{m = - \frac{1}{2} } }}\\ \underline{\boxed{ if \: y = \frac{2}{3} x\to \: the \: slope\to \boxed{m = \frac{2}{3} }}}\\ \)
a hybrid vehicle has a mileage rating of 22 km/l. what is the gas mileage in miles per gallon? (given: 1 mi
Answers
To convert kilometers per liter to miles per gallon, we need to use conversion factors. There are approximately 3.785 liters in a gallon, and there are approximately 1.609 kilometers in a mile.
So, first we convert the fuel efficiency of the hybrid vehicle from kilometers per liter to kilometers per gallon:
1 km/liter * 3.785 liters/gallon = 3.785 km/gallon
Then, we convert kilometers per gallon to miles per gallon:
3.785 km/gallon * 1 mile/1.609 km = 2.35 miles/gallon
Therefore, the gas mileage of the hybrid vehicle is approximately 2.35 miles per gallon.
It's worth noting that the mileage rating of a hybrid vehicle can vary depending on factors such as driving conditions and habits, so the actual gas mileage may differ from the stated rating. Additionally, the conversion factors used here are approximate, so the exact gas mileage may vary slightly depending on the specific conversion factors used.
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im a bit confused :(
Answers
Answer:
420
Step-by-step explanation:
the basic formula for volume is length × width × height.
multiply them all!
ig
Answer:
42
Step-by-step explanation:
For more information search volume for triangular prism and enter the numbers for the diagram
The intensity of exercise and your heart rate-positive-negative-no correlation
Answers
The intensity of excercise increases the heart rate, that is, more intensity the excersice, greater the heart rate.
It means that there is a positive correlation between int
Jaden made 6 L of corn soup for hid birthday a bowl can hold 200 ML of soup how many bowls can he fill
Answers
Answer:
30
Step-by-step explanation:
1L=1000
6L=?
6×1000= 6000ML
a soup can hold 200ML
6000/200
= 30
Step-by-step explanation:
Jaden has made a total of 6000 ML (6 L x 1000 ML/L = 6000 ML) of corn soup.
To find out how many bowls he can fill, we need to divide the total amount of soup by the amount of soup that can fit in one bowl.
6000 ML ÷ 200 ML/bowl = 30 bowls
Therefore, Jaden can fill 30 bowls with his 6 L of corn soup.
The figure below shows a 39-inch ramp that is attacked to a deck.
How high is the deck if the base of the ramp is 36 inches from the deck
Answers
Answer:
15 inches
Step-by-step explanation:
1. Use the Pythagorean Theorem: a^2+b^2=c^2
You are already given c (the longest side) and one of the legs which could be a or b.
2. Plug the numbers into the formula and square them.
a^2 + 36^2 = 39^2
Squaring the numbers gives you: a^2 + 1,296 = 1,521
3. Subtract 1,296 from both sides and take the square root of the result.
a^2 = 225
\(\sqrt{225}\) = 15
Answer: 15
Step-by-step explanation:
Write the equation of a line that is perpendicular to y = -8 3 x + 4 and goes through the point (5, 2)
Answers
Answer:
y = 3/8x + 1/8
Step-by-step explanation:
The slope of a perpendicular line is the opposite and reciprocal of the original slope.
-8/3 -> 3/8
Find the new y-intercept.
y = 3/8x + b
2 = 3/8(5) + b
2 = 1.875 + b
0.125 = b
y = 3/8x + 1/8
Best of Luck!
Help PLZZZ
Describe the change in the graph of the parabola f(x) when it transforms into g(x) = two thirdsf(x).
A The parabola g(x) will open in the opposite direction of f(x), and the parabola will be narrower than f(x).
BThe parabola g(x) will open in the same direction of f(x), and the parabola will be narrower than f(x).
CThe parabola g(x) will open in the opposite direction of f(x), and the parabola will be wider than f(x).
D The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Answers
Answer:
The parabola g(x) will open in the same direction of f(x), and the parabola will be wider than f(x).
Step-by-step explanation:
Answer:
It's B.
Step-by-step explanation:
I took the test.
**URGENT PLEASE HELP**
Find g(x), where g(x) is the translation 2 units right and 13 units down of f(x) = -2x + 5.
Answers
Answer:
g(x)=x+9
Step-by-step explanation:
When translating a graph, adding the number of units shifts the graph to the left and subtracting the number of units shifts it to the right. Since you need the graph translated 9 units to the left, you will need to add that many units to x
therefore, g(x)=x+9
Answer:
g(x)=x-8
Step-by-step explanation:
-2+2 = 0, so g(x) = x
5-13 = -8
how do you know if delta s is positive or negative?
Answers
The sign of ΔS should always be interpreted in the context of the specific process or reaction being considered
What are the rules of delta s positive or negative?The sign of ΔS (change in entropy) depends on the process or reaction being considered. Here are some general rules to determine the sign of ΔS:
If the number of products is greater than the number of reactants in a chemical reaction, ΔS is positive.If the number of products is less than the number of reactants, ΔS is negative.If a solid or a liquid dissolves in a solvent, ΔS is usually positive because the dissolved species have more freedom of movement in the solution than in the solid or liquid phase.If a gas is produced in a reaction, ΔS is usually positive because gases have more freedom of movement than liquids or solids.If a gas is consumed in a reaction, ΔS is usually negative because the reactants have more freedom of movement as separate gas molecules than as a condensed phase.If a system goes from a less disordered state to a more disordered state (e.g., from a solid to a liquid or a gas), ΔS is positive.If a system goes from a more disordered state to a less disordered state (e.g., from a gas to a liquid or a solid), ΔS is negative.It is important to note that these are general rules, and there can be exceptions. The sign of ΔS should always be interpreted in the context of the specific process or reaction being considered
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Market segmentation research is research that is used to help a firm identify
segments in a market, with the end goal of developing different types of pushpins
for the different segments (i. E. , market segmentation).
True
False
Answers
50 P0!NTS!
Favorite hobby/activity?
mines dirt biking
Answers
Answer:
Step-by-step explanation:
Favorite hobby is gaming
Favorite activity is football
A person invested \$150$150 in an account growing at a rate allowing the money to double every 13 years. How much money would be in the account after 22 years, to the nearest dollar?
Answers
Answer:
Amount after 22 year = $484.80 (Approx.)
Step-by-step explanation:
Given:
Amount deposit in bank = $150
Double in year = 13 year
Find:
Amount after 22 year
Computation:
A = P[1+r]ⁿ
Amount after 13 year = 2 x 150
Amount after 13 year = $300
300 = 150[1+r]¹³
2 = [1+r]¹³
Rate of interest = 5.477%
Amount after 22 year
A = P[1+r]ⁿ
Amount after 22 year = 150[1+5.477%]²²
Amount after 22 year = $484.80 (Approx.)
what is 2.16666666667 as a whole number