Q: For the point $$(12, 5) on $$the terminal side of angle $$\theta in $$standard position, what is $$\sin \theta$$?

$$\sin \theta = \dfrac{5}{13}$$

Q: For the point $$(8, -6) on $$the terminal side of angle $$\theta$$, what is $$\tan \theta$$?

$$\tan \theta = -\dfrac{3}{4}$$

Q: If $$\tan \theta = \dfrac{8}{5}$$ and $$\theta is in $$quadrant III, what is $$\sin \theta$$?

$$\sin \theta = -\dfrac{8}{89}$$

Q: If $$\sin \theta = -\dfrac{2}{3}$$ and $$\cos \theta \u003e 0$$, what is $$\tan \theta$$?

$$\tan \theta = -\dfrac{2\sqrt{5}}{5}$$

Q: If $$\cot \theta = -\dfrac{7}{24}$$ and $$\theta is in $$quadrant II, what is $$\sin \theta$$?

$$\sin \theta = \dfrac{24}{25}$$

Q: If $$\sec \theta = -\dfrac{25}{7}$$ and $$\theta is in $$quadrant II, what is $$\cos \theta$$?

$$\cos \theta = -\dfrac{7}{25}$$

Q: If $$\theta is in $$standard position and its terminal side passes through $$(0, -5)$$, which trigonometric functions are undefined?

$$\tan \theta$$ and $$\sec \theta$$

Q: If $$\theta is in $$quadrant IV, which trigonometric functions are positive?

$$\cos \theta$$ and $$\sec \theta$$

Question 1

Given two similar right triangles, one with legs of 42 in. and 63 in., and the other with legs of 38 ft and $$x ft$$, what is the value of $$x in $$feet? (Assume 1 ft = 12 in.)

Accepted Answer

$$x = 57$$

Question 2

For the point $$(12, 5) on $$the terminal side of angle $$	heta in $$standard position, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \dfrac{5}{13}$$

Question 3

For the point $$(8, -6) on $$the terminal side of angle $$	heta$$, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = -\dfrac{3}{4}$$

Question 4

Given the line $$3x - 2y = 0$$ and the point $$(-2, -3)$$, what is $$r ($$the distance from the origin to the point)?

Accepted Answer

$$r = \sqrt{13}$$

Question 5

For the point $$(5, 0) on $$the terminal side of angle $$	heta$$, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = 1$$

Question 6

For the point $$(0, -5) on $$the terminal side of angle $$	heta$$, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = -1$$

Question 7

If $$	an 	heta = \dfrac{8}{5}$$ and $$	heta is in $$quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = -\dfrac{8}{89}$$

Question 8

Which of the following is NOT a possible value for $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = -1.7$$

Question 9

If $$\sin 	heta = -\dfrac{2}{3}$$ and $$\cos 	heta \u003e 0$$, what is $$	an 	heta$$?

Accepted Answer

$$	an 	heta = -\dfrac{2\sqrt{5}}{5}$$

Question 10

A wheel spins at $$4.5$$ revolutions per second. How many degrees does a point on the edge of the wheel move in $$5$$ seconds?

Accepted Answer

$$8100^\circ$$

Question 11

If $$\cot 	heta = -\dfrac{7}{24}$$ and $$	heta is in $$quadrant II, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \dfrac{24}{25}$$

Question 12

Which quadrant contains angles where $$	an 	heta \u003e 0$$ and $$\csc 	heta \u003c 0$$?

Accepted Answer

Quadrant III

Question 13

If $$\sec 	heta = -\dfrac{25}{7}$$ and $$	heta is in $$quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = -\dfrac{7}{25}$$

Question 14

If $$	heta is in $$standard position and its terminal side passes through $$(0, -5)$$, which trigonometric functions are undefined?

Accepted Answer

$$	an 	heta$$ and $$\sec 	heta$$

Question 15

If $$	heta is in $$quadrant IV, which trigonometric functions are positive?

Accepted Answer

$$\cos 	heta$$ and $$\sec 	heta$$

Chapter 1: Trigonometric Functions – Angles, Triangles, and Trigonometric Definitions

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