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

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

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 $0 \leq \theta < 2\pi$ (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 $\cot 	heta < 0$, in which quadrant(s) could $	heta$ lie?

Accepted Answer

2nd and 4th quadrants

Question 4

If $	an 	heta > 0$ and $\cos 	heta < 0$, in which quadrant must $	heta$ be?

Accepted Answer

3rd quadrant

Question 5

If $\csc 	heta < 0$ and $\sec 	heta > 0$, 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 $\sin 	heta > 0$, 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

$	heta_1 = 49.1^\circ$, $	heta_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 $0 \leq 	heta < 2\pi$ (radians).

Accepted Answer

$	heta_1 = 0.670$ 	ext{ rad}, $	heta_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 $\cos 	heta > 0$ for $0^\circ < 	heta < 360^\circ$, what is the value of $	heta$?

Accepted Answer

$306.2^\circ$

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

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