Q: Find two angles $$\theta in$$ $$[0, 2\pi)$$ such that $$\tan \theta = -3.$$

$$\theta = \pi - \arctan(3), \theta = 2\pi - \arctan(3)$$

Question 1

Given the point $$(-8, 15) on $$the terminal side of an angle $$	heta in $$standard position, what is $$\sin 	heta$$?

Accepted Answer

$$\frac{15}{17}$$

Question 2

Which trigonometric functions are positive in Quadrant III?

Accepted Answer

Tangent and cotangent

Question 3

If $$\cos 	heta = -\frac{8}{17}$$ and $$	heta is in $$Quadrant III, what is $$\sin 	heta$$?

Accepted Answer

$$-\frac{15}{17}$$

Question 4

What is the reference angle for $$220^\circ$$?

Accepted Answer

$$40^\circ$$

Question 5

Find $$	an 	heta if $$the point $$(-2, -5) is on $$the terminal side of $$	heta.$$

Accepted Answer

$$\frac{5}{2}$$

Question 6

Which of the following is the correct definition of $$\sec 	heta$$ for an angle in standard position with terminal point $$(x, y)$$ and $$r = \sqrt{x^2$ + y^2$}$$?

Accepted Answer

$$\frac{r}{x}$$

Question 7

Evaluate $$\sin 300^\circ.$$

Accepted Answer

$$-\frac{1}{2}$$

Question 8

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

Accepted Answer

$$\frac{3}{5}$$

Question 9

Which of the following angles has a terminal side on the negative $$y-$$axis?

Accepted Answer

$$270^\circ$$

Question 10

A Ferris wheel rotates such that a seat makes an angle of $$230^\circ$$ with the positive $$x-$$axis. What is $$\sin 230^\circ$$ rounded to four decimal places?

Accepted Answer

$$-0.6428$$

Question 11

Find two angles $$	heta in$$ $$[0, 2\pi)$$ such that $$	an 	heta = -3.$$

Accepted Answer

$$	heta = \pi - \arctan(3), 	heta = 2\pi - \arctan(3)$$

Question 12

If $$\sin 	heta = -\frac{1}{2}$$ and $$0 \leq 	heta \u003c 2\pi$$, what are the possible values of $$	heta$$?

Accepted Answer

$$\frac{7\pi}{6}, \frac{11\pi}{6}$$

Question 13

Which trigonometric function is undefined for $$	heta = 90^\circ$$?

Accepted Answer

$$	an 	heta$$

Question 14

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 base is 6 ft from the wall, what is $$	an 	heta$$?

Accepted Answer

$$\frac{8}{6}$$

Question 15

Evaluate $$\sec 310^\circ to $$four decimal places.

Accepted Answer

$$1.6003$$

Question 16

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

Accepted Answer

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

Question 17

Which of the following is the correct value of $$	an \left(-\frac{\pi}{9}ight)$$ rounded to four decimal places?

Accepted Answer

$$-0.3491$$

Question 18

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

Accepted Answer

Cosine and secant

Question 19

A rotating radar antenna completes one full revolution every 10 seconds. What is the reference angle when the antenna has rotated $$250^\circ$$ from the positive $$x-$$axis?

Accepted Answer

$$70^\circ$$

Question 20

If $$\cot 1.35 is $$evaluated using a calculator, which of the following is closest to the answer (rounded to four decimal places)?

Accepted Answer

$$0.2160$$

Trigonometric Functions of Any Angle: Signs, Reference Angles, and Calculator Use

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