Q: Which of the following is the correct cofunction identity for $$\tan A in $$radians?

$$\tan A = \cot(\dfrac{\pi}{2} - A)$$

Question 1

Given a right triangle with side lengths 7 (opposite), 24 (adjacent), and 25 (hypotenuse), what is $$	an A$$ for angle $$A$$ opposite the side of length 7?

Accepted Answer

$$	an A = \dfrac{7}{24}$$

Question 2

Which of the following is the correct cofunction identity for $$\sin A$$ when $$A is $$measured in degrees?

Accepted Answer

$$\sin A = \cos(90^\circ - A)$$

Question 3

Find the reference angle for $$218^\circ.$$

Accepted Answer

$$38^\circ$$

Question 4

What is the value of $$\sin 60^\circ$$?

Accepted Answer

$$\dfrac{\sqrt{3}}{2}$$

Question 5

If $$\cos 	heta = -\dfrac{\sqrt{2}}{2}$$ and $$	heta is in$$ $$[0^\circ, 360^\circ)$$, which of the following are possible values for $$	heta$$?

Accepted Answer

$$135^\circ$$ and $$225^\circ$$

Question 6

Which trigonometric function is positive in quadrant II?

Accepted Answer

Sine

Question 7

Find the exact value of $$	an 210^\circ.$$

Accepted Answer

$$-\dfrac{\sqrt{3}}{3}$$

Question 8

A car weighing 3000 pounds has a grade resistance of 500 pounds. What is the angle $$	heta of $$the incline? (Use $$F = W \sin 	heta)$$

Accepted Answer

$$	heta \approx 9.6^\circ$$

Question 9

Which of the following is the correct cofunction identity for $$	an A in $$radians?

Accepted Answer

$$	an A = \cot(\dfrac{\pi}{2} - A)$$

Question 10

If $$\sin 	heta = 0.9677091705$$, what is $$	heta in $$degrees?

Accepted Answer

$$	heta \approx 75.4^\circ$$

Question 11

Find the six trigonometric function values for $$60^\circ.$$

Accepted Answer

$$\sin 60^\circ = \dfrac{\sqrt{3}}{2}, \cos 60^\circ = \dfrac{1}{2}, 	an 60^\circ = \sqrt{3}, \csc 60^\circ = \dfrac{2}{\sqrt{3}}, \sec 60^\circ = 2, \cot 60^\circ = \dfrac{\sqrt{3}}{3}$$

Question 12

If $$	an 	heta = 1$$, what is the acute angle $$	heta in $$degrees?

Accepted Answer

$$	heta = 45^\circ$$

Question 13

Which of the following is the correct definition of $$\cot A in $$terms of a right triangle?

Accepted Answer

$$\cot A = \dfrac{x}{y}$$

Question 14

Find the reference angle for $$\dfrac{5\pi}{6}$$ radians.

Accepted Answer

$$\dfrac{\pi}{6}$$

Question 15

If $$\cos 	heta = 0.3623577545$$ and $$	heta is in$$ $$[0, 2\pi)$$, what is the second solution for $$	heta$$?

Accepted Answer

$$	heta = 2\pi - 1.2$$

Question 16

Which of the following is the correct process for finding the trigonometric function value for any nonquadrantal angle $$	heta$$?

Accepted Answer

Find a coterminal angle, find the reference angle, use the function value for the reference angle, and determine the correct sign based on the quadrant.

Question 17

If $$\cos 49^\circ 12' is $$calculated using a calculator, which of the following is closest to the value?

Accepted Answer

$$0.656$$

Right Triangles and Evaluating Trigonometric Functions

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