Question 1

Find the exact value of the expression.&#10;

Accepted Answer

The function $\tan^{-1}(1)$ asks for the angle whose tangent is 1. The tangent of an angle is equal to 1 when the angle is $\frac{\pi}{4}$ radians (or 45 degrees), which is in the first quadrant where both sine and cosine are positive, and their absolute values are equal, making the tangent (sin/cos) equal to 1.

Question 2

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

A

Question 3

Use a calculator to find the value of the expression rounded to two decimal places.&#10;

Accepted Answer

B

Question 4

Find the exact value of the expression.&#10;

Accepted Answer

$\sin^{-1}(0.5)$ corresponds to the angle whose sine is 0.5, which is $\frac{\pi}{6}$ or 30 degrees in the principal value range of arcsin, which is $[- \frac{\pi}{2}, \frac{\pi}{2}]$.

Question 5

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The cosine function is even, so $\cos(-\frac{3\pi}{5}) = \cos(\frac{3\pi}{5})$. The range of $\cos^{-1}$ is $[0, \pi]$, so $\cos^{-1}(\cos(\frac{3\pi}{5})) = \frac{3\pi}{5}$.

Question 6

Use a calculator to find the value of the expression rounded to two decimal places.&#10;

Accepted Answer

The inverse sine function, $\sin^{-1}$, gives the angle whose sine is the given value. Calculating $\sin^{-1}(\frac{\sqrt{5}}{5})$ using a calculator gives approximately 0.46 radians.

Question 7

Find the exact value of the expression.&#10;

Accepted Answer

The value of $\cos^{-1}\frac{\sqrt{3}}{2}$ corresponds to the angle whose cosine is $\frac{\sqrt{3}}{2}$. This is the angle $\frac{\pi}{6}$ or 30 degrees in the unit circle.

Question 8

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The expression $\cos \left[ \cos ^ { - 1 } ( - 0.9372 ) \right]$ simplifies directly to $-0.9372$ because $\cos^{-1}$ is the inverse function of $\cos$, meaning it will return the original value inside the cosine inverse function when applied.

Question 9

Find the exact value of the expression.&#10;

Accepted Answer

The value of $\sin^{-1}\frac{\sqrt{2}}{2}$ corresponds to the angle whose sine is $\frac{\sqrt{2}}{2}$. This is known to be $\frac{\pi}{4}$ or 45 degrees in the first quadrant where sine values are positive.

Question 10

Use a calculator to find the value of the expression rounded to two decimal places.&#10;

Accepted Answer

The inverse sine function, $\sin^{-1}$, gives the angle whose sine is the given number. Using a calculator, $\sin^{-1}(-\frac{1}{7})$ is approximately $-0.14$ radians.

Question 11

Use a calculator to find the value of the expression rounded to two decimal places.&#10;

Accepted Answer

The answer of Use a calculator to find the value...

Question 12

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The answer of Find the exact value of the expression....

Question 13

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The answer of Find the exact value of the expression....

Question 14

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The answer of Find the exact value of the expression....

Question 15

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The answer of Find the exact value of the expression....

Question 16

Use a calculator to find the value of the expression rounded to two decimal places.&#10;

Accepted Answer

The answer of Use a calculator to find the value...

Question 17

Use a calculator to find the value of the expression rounded to two decimal places.&#10;

Accepted Answer

The answer of Use a calculator to find the value...

Question 18

Find the exact value of the expression.&#10;

Accepted Answer

The answer of Find the exact value of the expression.&#10;...

Question 19

Use a calculator to find the value of the expression rounded to two decimal places.&#10;

Accepted Answer

The answer of Use a calculator to find the value...

Question 20

Find the exact value of the expression.&#10;

Accepted Answer

The answer of Find the exact value of the expression.&#10;...

Question 21

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 22

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 23

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

The answer of Find the domain of the function f...

Question 24

Find the exact solution of the equation.&#10;

Accepted Answer

The answer of Find the exact solution of the equation.&#10;...

Question 25

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 26

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

The answer of Find the domain of the function f...

Question 27

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 28

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The answer of Find the exact value of the expression....

Question 29

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The answer of Find the exact value of the expression....

Question 30

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 31

Find the exact value of the expression. Do not use a calculator.&#10;

Accepted Answer

The answer of Find the exact value of the expression....

Question 32

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

The answer of Find the domain of the function f...

Question 33

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 34

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

The answer of Find the domain of the function f...

Question 35

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

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Question 36

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

The answer of Find the domain of the function f...

Question 37

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

The answer of Find the domain of the function f...

Question 38

Find the domain of the function f and of its inverse function f-1.&#10;

Accepted Answer

The answer of Find the domain of the function f...

Question 39

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 40

Find the inverse function f-1 of the function f.&#10;

Accepted Answer

The answer of Find the inverse function f-1 of the...

Question 41

Find the exact solution of the equation.&#10;

Accepted Answer

The answer of Find the exact solution of the equation.&#10;...

Question 42

Find the exact solution of the equation.&#10;

Accepted Answer

The answer of Find the exact solution of the equation.&#10;...

Question 43

Write the word or phrase that best completes each statement or answers the question.&#10;Solve the problem.&#10;  orth

Accepted Answer

The answer of Write the word or phrase that best...

Question 44

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 45

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 46

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 47

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

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Question 48

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 49

Find the exact solution of the equation.&#10;

Accepted Answer

The answer of Find the exact solution of the equation.&#10;...

Question 50

Write the word or phrase that best completes each statement or answers the question.
Solve the problem.

can be used to approximate the number of hours of daylight when the declination of the sun is i orth

latitude for any date between the vernal equinox and autumnal equinox. To use this formula,

must be expressed in radians. Approximate the number of hours of daylight in Fargo, North Dakota,
for vernal equinox

Accepted Answer

The answer of Write the word or phrase that best...

Question 51

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 52

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 53

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 54

Find the exact solution of the equation.&#10;

Accepted Answer

The answer of Find the exact solution of the equation.&#10;...

Question 55

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 56

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 57

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 58

Find the exact solution of the equation.&#10;

Accepted Answer

The answer of Find the exact solution of the equation.&#10;...

Question 59

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 60

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 61

Find the exact value of the composition.&#10;

Accepted Answer

The answer of Find the exact value of the composition.&#10;...

Question 62

Write the trigonometric expression as an algebraic expression in u.&#10;

Accepted Answer

The answer of Write the trigonometric expression as an algebraic...

Question 63

Choose the one alternative that best completes the statement or answers the question.&#10;Find the exact value of the expression.&#10;

Accepted Answer

The answer of Choose the one alternative that best completes...

Question 64

Find the exact value of the composition.&#10;

Accepted Answer

The answer of Find the exact value of the composition.&#10;...

Deck 6: Analytic Trigonometry