Question 1

Given a point $$P = (x, y) on $$the terminal side of an angle $$	heta in $$standard position, which of the following correctly defines $$\sin 	heta$$ for any angle?

Accepted Answer

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

Question 2

Which trigonometric functions are always positive in Quadrant III?

Accepted Answer

Tangent and cotangent

Question 3

If $$	heta = 225^\circ$$, what is the reference angle?

Accepted Answer

$$45^\circ$$

Question 4

A surveyor measures an angle of $$480^\circ$$ from the positive $$x-$$axis. What is the reference angle?

Accepted Answer

$$60^\circ$$

Question 5

Which of the following is the correct value of $$\cos 270^\circ$$?

Accepted Answer

$$0$$

Question 6

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

Accepted Answer

$$-\dfrac{4}{5}$$

Question 7

A Ferris wheel rotates such that a seat is at an angle of $$135^\circ$$ from the positive $$x-$$axis. Which trigonometric functions are positive at this position?

Accepted Answer

Sine and cosecant

Question 8

Find $$	an 180^\circ.$$

Accepted Answer

$$0$$

Question 9

If $$	heta is an $$angle in standard position and $$	an 	heta is $$negative, in which quadrants could $$	heta$$ lie?

Accepted Answer

Quadrants II and IV

Question 10

A ladder leans against a wall making an angle of $$210^\circ$$ with the positive $$x-$$axis. What is the sign of $$\cos 210^\circ$$?

Accepted Answer

Negative

Question 11

Given $$	heta = -120^\circ$$, what is the reference angle?

Accepted Answer

$$60^\circ$$

Question 12

If $$\cos 	heta = 0$$ and $$	heta is $$between $$0^\circ$$ and $$360^\circ$$, what are the possible values for $$	heta$$?

Accepted Answer

$$90^\circ$$ and $$270^\circ$$

Question 13

A rotating wind vane points at $$330^\circ. $$What is the reference angle?

Accepted Answer

$$30^\circ$$

Question 14

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

Accepted Answer

$$-\dfrac{12}{13}$$

Question 15

Which of the following is the correct definition of $$	an 	heta$$ for any angle?

Accepted Answer

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

Question 16

A satellite orbits Earth and forms an angle of $$405^\circ$$ with the positive $$x-$$axis. What is the reference angle?

Accepted Answer

$$45^\circ$$

Question 17

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

Accepted Answer

Cosine and secant

Question 18

Find $$\csc 0^\circ.$$

Accepted Answer

Undefined

Question 19

If $$	an 	heta = 1$$ and $$	heta is $$between $$0^\circ$$ and $$360^\circ$$, what are the possible values for $$	heta$$?

Accepted Answer

$$45^\circ$$ and $$225^\circ$$

Trigonometric Functions of Any Angle

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