Q: Which trigonometric functions are positive in the third quadrant according to the CAST rule?

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

Q: Find the reference angle $$\theta_{\text{ref}}$$ for $$\theta = 330^\circ.$$

$$\theta_{\text{ref}} = 30^\circ$$

Q: If $$\sin \theta = 0.7561$$ for $$0^\circ \leq \theta \u003c 360^\circ$$, what are the two possible values for $$\theta$$?

$$\theta = 49.1^\circ,\ 130.9^\circ$$

Q: If $$\tan \theta = -1.830$$ for $$0^\circ \leq \theta \u003c 360^\circ$$, what are the two possible values for $$\theta$$?

$$\theta = 118.7^\circ,\ 298.7^\circ$$

Question 1

Which trigonometric functions are positive in the third quadrant according to the CAST rule?

Accepted Answer

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

Question 2

Without using a calculator, determine the sign of $$	an 320^\circ.$$

Accepted Answer

Negative

Question 3

If $$\cos 	heta = -0.4025$$ and $$0^\circ \leq 	heta \u003c 360^\circ$$, in which quadrants does $$	heta$$ lie?

Accepted Answer

Quadrants II and III

Question 4

Find the reference angle $$	heta_{	ext{ref}}$$ for $$	heta = 330^\circ.$$

Accepted Answer

$$	heta_{	ext{ref}} = 30^\circ$$

Question 5

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

Accepted Answer

$$	heta = 306.2^\circ$$

Question 6

A circular garden has a radius of $$4.0 m. $$What is the length of the arc subtended by a central angle of $$120^\circ$$?

Accepted Answer

$$s = 8.38 m$$

Question 7

A sector of a circle has a central angle of $$160^\circ$$ and an arc length of $$11.6 cm. $$What is the area of the sector?

Accepted Answer

$$A = 24.05 cm$^2$$

Question 8

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

Accepted Answer

$$v = 136.8 m/$$min

Question 9

Convert an angular velocity of $$13.5$$ rev/min to radians per second.

Accepted Answer

$$1.41$$ rads/sec

Question 10

A pulley wheel of radius $$0.19 m $$rotates so that $$7.5 m of $$rope passes around it in $$15$$ seconds. What is the RPM (revolutions per minute) of the pulley?

Accepted Answer

$$25.13$$ RPM

Question 11

If a sector of a circle has an area of $$75.5 m$^2$$ and a radius of $$12.2 m$$, what is the central angle in radians?

Accepted Answer

$$	heta = 1.01$$

Question 12

A vehicle travels at $$5.6 km/h on $$tires with a diameter of $$3.66 m. $$What is the angular velocity of the tire in radians per minute?

Accepted Answer

$$\omega = 51.00$$ rads/min

Question 13

Which formula correctly relates linear velocity $$v$$ and angular velocity $$\omega$$ for a point at radius $$r$$ from the center of rotation?

Accepted Answer

$$v = r \omega$$

Question 14

A spotlight beam sweeps through a horizontal angle of $$75.0^\circ$$ with a range of $$110 m. $$What area can it cover?

Accepted Answer

$$A = 7919 m$^2$$

Question 15

If $$\sin 	heta = 0.7561$$ for $$0^\circ \leq 	heta \u003c 360^\circ$$, what are the two possible values for $$	heta$$?

Accepted Answer

$$	heta = 49.1^\circ,\ 130.9^\circ$$

Question 16

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

$$A = 0.690 m$^2$$

Question 17

If $$	an 	heta = -1.830$$ for $$0^\circ \leq 	heta \u003c 360^\circ$$, what are the two possible values for $$	heta$$?

Accepted Answer

$$	heta = 118.7^\circ,\ 298.7^\circ$$

Question 18

A pulley belt $$4.00 m $$long takes $$2.00$$ seconds to make one complete revolution around a pulley of radius $$20.0 cm. $$What is the linear velocity?

Accepted Answer

$$v = 2.00 m/s$$

Trigonometric Functions of Any Angle, Radian Measure, and Angular Velocity

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