Q: In which quadrant does the angle $$320^\ ext{o}$$ lie, and what is the sign of $$\tan 320^\ ext{o}$$?

4th quadrant; $$\tan 320^\ ext{o} is $$negative

Q: If $$\sec \theta = -1.784$$, what is the reference angle $$\theta_\text{ref}$$?

$$\theta_\text{ref} = \cos$$^{-1}$$(0.5604) = 55.9^\circ$$

Q: Find the two values for $$\theta$$ for $$\sin \theta = 0.621$$ for $$0 \leq \theta \u003c 2\pi ($$radians).

$$\$$theta_1$$ = 0.670$$ \text{ rad}, $$\$$theta_2$$ = 2.47$$ \text{ rad}$

Question 1

In which quadrant does the angle $$320^\	ext{o}$$ lie, and what is the sign of $$	an 320^\	ext{o}$$?

Accepted Answer

4th quadrant; $$	an 320^\	ext{o} is $$negative

Question 2

Given $$\csc 115^\	ext{o}$$, which quadrant does the angle lie in and what is the sign of $$\csc 115^\	ext{o}$$?

Accepted Answer

2nd quadrant; $$\csc 115^\	ext{o} is $$positive

Question 3

If $$\cot 	heta \u003c 0$$, in which quadrant(s) could $$	heta$$ lie?

Accepted Answer

2nd and 4th quadrants

Question 4

If $$	an 	heta \u003e 0$$ and $$\cos 	heta \u003c 0$$, in which quadrant must $$	heta be$$?

Accepted Answer

3rd quadrant

Question 5

If $$\csc 	heta  0$$, in which quadrant must $$	heta be$$?

Accepted Answer

4th quadrant

Question 6

If $$\sin 	heta = 0.34050$$, in which quadrant(s) could $$	heta$$ lie?

Accepted Answer

1st and 2nd quadrants

Question 7

If $$\cos 	heta = 0.2399$$ and $$\sin 	heta \u003e 0$$, in which quadrant must $$	heta be$$?

Accepted Answer

1st quadrant

Question 8

Find the two values for $$	heta$$ for $$\sin 	heta = 0.7561$$ for $$0^\circ \leq 	heta \leq 360^\circ.$$

Accepted Answer

$$\$$theta_1$$ = 49.1^\circ$$, $$\$$theta_2$$ = 130.9^\circ$$

Question 9

A DVD has a diameter of $$12.1 cm $$and rotates at $$360.0$$ rev/min. What is the linear velocity at a point on the outer edge in m/min?

Accepted Answer

$$136.8 m/$$min

Question 10

A section of sidewalk is a circular sector of radius $$1.25 m $$and central angle $$50.6^\circ. $$What is the area of this section?

Accepted Answer

$$0.690 m$^2$$

Question 11

While playing, the left spool of a VCR turns through $$820^\circ. $$For this part of the tape, it is $$3.30 cm $$from the centre of the spool to the tape. What length of tape is played?

Accepted Answer

$$47.2 cm$$

Question 12

A pulley has a radius of $$20.0 cm. If a $$belt moves $$4.00 m in$$ $$2.00 s$$, what is the linear velocity of the belt?

Accepted Answer

$$2.0 m/s$$

Question 13

A special vehicle for travelling on glacial ice has tires that are $$3.66 m in $$diameter. If the vehicle travels at $$5.6 km/h$$, what is the angular velocity of the tire in rad/min?

Accepted Answer

$$51$$ 	ext{ rad/min}$

Question 14

If $$\sec 	heta = -1.784$$, what is the reference angle $$	heta_	ext{ref}$$?

Accepted Answer

$$	heta_	ext{ref} = \cos$$^{-1}$$(0.5604) = 55.9^\circ$$

Question 15

Find the two values for $$	heta$$ for $$\sin 	heta = 0.621$$ for $$0 \leq 	heta \u003c 2\pi ($$radians).

Accepted Answer

$$\$$theta_1$$ = 0.670$$ 	ext{ rad}, $$\$$theta_2$$ = 2.47$$ 	ext{ rad}$

Question 16

What is the central angle in radians if the area of a sector is $$75.5 m$^2$$ and the radius is $$12.2 m$$?

Accepted Answer

$$1.01$$ 	ext{ rad}$

Question 17

If $$	an 	heta = -1.366$$ and $$\cos 	heta \u003e 0$$ for $$0^\circ \u003c 	heta \u003c 360^\circ$$, what is the value of $$	heta$$?

Accepted Answer

$$306.2^\circ$$

Trigonometric Functions and Applications: Signs, Quadrants, and Circular Motion

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드