Q: Which of the following is a cofunction identity for $$\cos \theta$$?

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

Q: A highway has a grade resistance of 500 pounds for a 3000-pound car. If grade resistance is modeled by $$R = W \sin \theta$$, what is the angle $$\theta of $$the incline?

$$\theta = \sin$$^{-1}$$\left(\frac{500}{3000}\right)$$

Q: If $$\tan \theta = 0.25$$ and $$\theta is $$measured in radians, what is $$\theta$$?

$$\theta = \tan$$^{-1}$$(0.25)$$

Q: Which of the following is the correct expression for the cofunction of $$\tan \theta$$?

$$\tan \theta = \cot(90^\circ - \theta)$$

Question 1

Given a right triangle with sides of length 7 (opposite), 24 (adjacent), and 25 (hypotenuse), what is the value of $$\sin A$$?

Accepted Answer

$$\frac{7}{25}$$

Question 2

What is the exact value of $$	an 60^\circ$$?

Accepted Answer

$$\sqrt{3}$$

Question 3

Which of the following is a cofunction identity for $$\cos 	heta$$?

Accepted Answer

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

Question 4

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

Accepted Answer

$$38^\circ$$

Question 5

If $$	heta = 210^\circ$$, what is the reference angle?

Accepted Answer

$$30^\circ$$

Question 6

What is the value of $$\cos(-240^\circ)$$?

Accepted Answer

$$-\frac{1}{2}$$

Question 7

Which quadrant does the angle $$225^\circ$$ lie in, and what is the sign of $$\sin 225^\circ$$?

Accepted Answer

Quadrant III, negative

Question 8

A highway has a grade resistance of 500 pounds for a 3000-pound car. If grade resistance is modeled by $$R = W \sin 	heta$$, what is the angle $$	heta of $$the incline?

Accepted Answer

$$	heta = \sin$$^{-1}$$\left(\frac{500}{3000}ight)$$

Question 9

Find all values of $$	heta in$$ $$[0^\circ, 360^\circ)$$ such that $$\cos 	heta = -\frac{\sqrt{2}}{2}.$$

Accepted Answer

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

Question 10

What is the value of $$\sin 30^\circ$$?

Accepted Answer

$$\frac{1}{2}$$

Question 11

If $$	an 	heta = 0.25$$ and $$	heta is $$measured in radians, what is $$	heta$$?

Accepted Answer

$$	heta = 	an$$^{-1}$$(0.25)$$

Question 12

Which trigonometric function is positive in quadrant II?

Accepted Answer

Sine

Question 13

What is the value of $$\cot 45^\circ$$?

Accepted Answer

$$1$$

Question 14

If $$	heta = 675^\circ$$, what is the reference angle?

Accepted Answer

$$45^\circ$$

Question 15

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

Accepted Answer

$$\frac{2}{\sqrt{3}}$$

Question 16

Which of the following is the correct expression for the cofunction of $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \cot(90^\circ - 	heta)$$

Question 17

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

Accepted Answer

$$	heta = 2\pi - 1.2$$

Question 18

What is the value of $$\sin 45^\circ$$?

Accepted Answer

$$\frac{\sqrt{2}}{2}$$

Question 19

A triangle has angles $$30^\circ$$, $$60^\circ$$, and $$90^\circ$$ with the side opposite $$30^\circ$$ equal to 1. What is the length of the side opposite $$60^\circ$$?

Accepted Answer

$$\sqrt{3}$$

Chapter 9: The Unit Circle and the Functions of Trigonometry – Study Notes

스터디 가이드 - 연습 문제

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