Q: Which trigonometric functions are positive in Quadrant III?

$$\tan \theta$$ and $$\cot \theta$$

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

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

Q: Which of the following is a reciprocal identity?

$$\sec \theta = \frac{1}{\cos \theta}$$

Question 1

Given the point $$(-3, 4) in $$the coordinate plane, which quadrant does this point lie in?

Accepted Answer

Quadrant II

Question 2

Given the point $$(0, -5) in $$the coordinate plane, where is this point located?

Accepted Answer

On the negative $$y-$$axis

Question 3

If $$\sin 	heta = -\frac{2}{3}$$ and $$	heta is in $$the quadrant where sine is negative and cosine is positive, which quadrant is $$	heta in$$?

Accepted Answer

Quadrant IV

Question 4

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

$$	an 	heta$$ and $$\cot 	heta$$

Question 5

If $$	an 	heta \u003e 0$$ and $$\csc 	heta \u003c 0$$, in which quadrant(s) could $$	heta be$$?

Accepted Answer

Quadrant III

Question 6

Given $$\cos 	heta = -\frac{2}{\sqrt{20}}$$, what is $$\sec 	heta$$?

Accepted Answer

$$-\sqrt{5}$$

Question 7

Which of the following is an impossible value for a trigonometric function?

Accepted Answer

$$\cos 	heta = -1.7$$

Question 8

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

Accepted Answer

Question 9

Given $$\cot 	heta = -\frac{7}{24}$$ and $$	heta is in $$Quadrant II, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{24}{25}$$

Question 10

Which identity is represented by $$	an 	heta = \frac{\sin 	heta}{\cos 	heta}$$?

Accepted Answer

Quotient Identity

Question 11

If $$\sin 	heta = -\frac{2}{3}$$, what is $$\csc 	heta$$?

Accepted Answer

$$-\frac{3}{2}$$

Question 12

Which of the following is the correct Pythagorean identity?

Accepted Answer

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

Question 13

If $$\cos 	heta = \frac{3}{5}$$ and $$	heta is in $$Quadrant I, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{4}{5}$$

Question 14

If $$	an 	heta = 1.8$$, what is $$\cot 	heta$$?

Accepted Answer

$$\frac{1}{1.8}$$

Question 15

Which of the following is a reciprocal identity?

Accepted Answer

$$\sec 	heta = \frac{1}{\cos 	heta}$$

Question 16

A ladder leans against a wall making an angle $$	heta$$ with the ground. If $$\sin 	heta = 0.6$$ and the ladder is $$10 ft $$long, how high up the wall does the ladder reach?

Accepted Answer

$$6 ft$$

Question 17

If $$\cos 	heta = 0$$, what is $$\sec 	heta$$?

Accepted Answer

Undefined

Question 18

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

Accepted Answer

Quadrant II

Question 19

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

Accepted Answer

$$-\frac{8}{\sqrt{89}}$$

Trigonometric Function Identities and Their Properties

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