Q: If $$\sin \theta = \dfrac{5}{13}$$ and $$\theta is in $$Quadrant II, what is $$\cos \theta$$?

$$\cos \theta = -\dfrac{12}{13}$$

Q: A ladder leans against a wall, forming an angle $$\theta$$ with the ground. If the top of the ladder is 8 ft above the ground and the ladder is 10 ft long, what is $$\sin \theta$$?

$$\sin \theta = \dfrac{8}{10}$$

Q: Which of the following is a correct Pythagorean identity?

$$\sin^2$ \theta + \cos^2$ \theta = 1$$

Q: If $$\tan \theta = 3$$ and $$\sec \theta \u003c 0$$, what is the value of $$\sec \theta$$?

$$\sec \theta = -\dfrac{\sqrt{10}}{1}$$

Q: If $$\sin \theta = \dfrac{4}{5}$$ and $$\theta is in $$Quadrant II, what is $$\tan \theta$$?

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

Q: If $$\theta is an $$angle in standard position and its terminal side passes through $$(6, 8)$$, what is $$\sec \theta$$?

$$\sec \theta = \dfrac{10}{6}$$

Q: Which of the following is true about the signs of trigonometric functions in Quadrant III?

$$\sin \theta$$ and $$\cos \theta$$ are negative, $$\tan \theta is $$positive

Question 1

A point $$(x, y)$$ lies on the terminal side of angle $$	heta in $$standard position, and $$r = \sqrt{x^2$ + y^2$}. $$Which of the following correctly expresses $$\sin 	heta in $$terms of $$x$$, $$y$$, and $$r$$?

Accepted Answer

$$\sin 	heta = \dfrac{y}{r}$$

Question 2

Given the point $$(3, -4) on $$the terminal side of angle $$	heta$$, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = \dfrac{3}{5}$$

Question 3

If $$\sin 	heta = \dfrac{5}{13}$$ and $$	heta is in $$Quadrant II, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = -\dfrac{12}{13}$$

Question 4

Which quadrant contains angles $$	heta$$ where $$\sin 	heta is $$positive and $$\cos 	heta is $$negative?

Accepted Answer

Quadrant II

Question 5

On the unit circle, what are the coordinates of the point corresponding to angle $$	heta$$?

Accepted Answer

$$(\cos 	heta, \sin 	heta)$$

Question 6

Given $$	an 	heta = \dfrac{y}{x}$$ and $$x \u003e 0$$, $$y \u003c 0$$, in which quadrant does $$	heta$$ lie?

Accepted Answer

Quadrant IV

Question 7

If $$\sin 	heta = -\dfrac{4}{5}$$ and $$	heta is in $$Quadrant III, what is $$	an 	heta$$?

Accepted Answer

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

Question 8

A ladder leans against a wall, forming an angle $$	heta$$ with the ground. If the top of the ladder is 8 ft above the ground and the ladder is 10 ft long, what is $$\sin 	heta$$?

Accepted Answer

$$\sin 	heta = \dfrac{8}{10}$$

Question 9

Which of the following is a correct Pythagorean identity?

Accepted Answer

$$\sin^2$ 	heta + \cos^2$ 	heta = 1$$

Question 10

If $$	an 	heta = 3$$ and $$\sec 	heta \u003c 0$$, what is the value of $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = -\dfrac{\sqrt{10}}{1}$$

Question 11

A point $$(x, y) is on $$the unit circle. If $$x = -\dfrac{3}{5}$$ and $$y \u003e 0$$, what is the quadrant of the point?

Accepted Answer

Quadrant II

Question 12

Given $$\sin 	heta = \dfrac{y}{r}$$ and $$\cos 	heta = \dfrac{x}{r}$$, which formula gives $$	an 	heta$$?

Accepted Answer

$$	an 	heta = \dfrac{y}{x}$$

Question 13

If $$\sin 	heta = \dfrac{4}{5}$$ and $$	heta is in $$Quadrant II, what is $$	an 	heta$$?

Accepted Answer

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

Question 14

Which of the following is true for all points $$(x, y) on $$the unit circle?

Accepted Answer

$$x^2$$ + $$y^2 = 1$

Question 15

If $$	heta is an $$angle in standard position and its terminal side passes through $$(6, 8)$$, what is $$\sec 	heta$$?

Accepted Answer

$$\sec 	heta = \dfrac{10}{6}$$

Question 16

A Ferris wheel has a radius of 20 meters. If a seat is at an angle $$	heta$$ such that $$\sin 	heta = 0.5$$, what is the vertical height of the seat above the center?

Accepted Answer

$$10$$ meters

Question 17

Which of the following is the correct expression for $$\cot 	heta in $$terms of $$x$$ and $$y$$?

Accepted Answer

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

Question 18

If $$\sin 	heta = -\dfrac{3}{5}$$ and $$	heta is in $$Quadrant IV, what is $$\cos 	heta$$?

Accepted Answer

$$\cos 	heta = \dfrac{4}{5}$$

Question 19

Which of the following is true about the signs of trigonometric functions in Quadrant III?

Accepted Answer

$$\sin 	heta$$ and $$\cos 	heta$$ are negative, $$	an 	heta is $$positive

Question 20

A point $$(x, y) is on $$the terminal side of $$	heta$$ with $$x \u003c 0$$ and $$y \u003c 0. $$Which quadrant is $$	heta in$$?

Accepted Answer

Quadrant III

Trigonometric Functions from the Unit Circle and Right Triangles

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