Q: If $$\sec \theta = -\dfrac{5}{4}$$ and $$\theta is in $$Quadrant III, what is $$\cos \theta$$?

$$\cos \theta = -\dfrac{4}{5}$$

Q: Given $$\sec \theta = -\dfrac{5}{4}$$ and $$\theta in $$Quadrant III, what is $$\sin \theta$$?

$$\sin \theta = -\dfrac{3}{5}$$

Q: If $$\theta is in $$Quadrant III, which of the following statements is true?

$$\sin \theta$$ and $$\cos \theta$$ are both negative

Question 1

Given a point $$(x, y) on $$the terminal side of an 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

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

$$\sin 	heta = -\dfrac{3}{5}$$

Question 5

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

Accepted Answer

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

Question 6

What is the reference angle for $$155^\circ$$?

Accepted Answer

$$25^\circ$$

Question 7

Find the value of $$	an 2115^\circ.$$

Accepted Answer

$$-1$$

Question 8

If $$	an 	heta = \dfrac{y}{x}$$, which of the following is true for $$	heta in $$standard position?

Accepted Answer

$$x$$ and $$y$$ are the coordinates of a point on the terminal side of $$	heta$$

Question 9

Which trigonometric function is always positive in Quadrant II?

Accepted Answer

$$\sin 	heta$$

Question 10

If a point $$(x, y) is on $$the terminal side of $$	heta$$ and $$r = \sqrt{x^2$ + y^2$}$$, what is $$\csc 	heta$$?

Accepted Answer

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

Question 11

Which of the following is the correct expression for $$r in $$terms of $$x$$ and $$y$$?

Accepted Answer

$$r = \sqrt{x^2$ + y^2$}$$

Question 12

If $$	heta is in $$Quadrant III, which of the following statements is true?

Accepted Answer

$$\sin 	heta$$ and $$\cos 	heta$$ are both negative

Question 13

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

Accepted Answer

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

Question 14

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

Accepted Answer

$$-\dfrac{3}{5}$$

Question 15

Which of the following is the correct definition of $$\sec 	heta in $$terms of $$r$$ and $$x$$?

Accepted Answer

$$\sec 	heta = \dfrac{r}{x}$$

Precalculus: Trigonometric Functions, Reference Angles, and Quadrant Analysis

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