Trigonometric Functions Review

Radians/ Degrees

100

Convert 45° to radians.

pi/4

200

Convert 7pi/6 radians to degrees.

210°

300

Express the angle 123.48° in degree–minute–second form.

123° 28' 48"

400

Give a positive and negative coterminal  angle for −pi/4.

-9pi/4 and 7pi/4

500

A circular sector has an area of 15pi square units and a central angle of 75°; what is the circle's exact radius in radical form?

6 sqrt(2)

Angular Speed and Distance

100

If a wheel of radius 2m rotates at 3 radians per second, what is the linear speed of a point on its rim?

6 m/s

200

A point on the edge of a flywheel with a radius of 10 inches is rotating at an angular speed of 5 radians per second; this is its linear speed in inches per second.

50 in/s

300

A ceiling fan with a radius of 2 feet is spinning at a rate of 120 revolutions per minute (RPM); findits angular speed expressed in radians per second.

4pi rad/s = 12.57 rad/s

400

A Ferris wheel of radius 15 m makes one full revolution every 40 seconds. Find its angular speed in radians per second.

Angular speed: pi/20 rad/s or 0.157rad/s

500

A Ferris wheel of radius 15 m makes one full revolution every 40 seconds. Find the linear speed of a seat in m/sec.

linear speed: 3pi/4 m/s = 2.36 m/s

Triangle Trig

100

In a right triangle, if sin⁡θ=3/5, find cosθ.

cosθ=4/5

200

In triangle ABC: given sides a = 8, b = 7, and included angle C = 60°, find side c.

sqrt(57) = 7.55

300

Find angle A if side a = 14, side b = 10, and angle B = 40°. State any ambiguity if present.

64.15° or 115.85°

400

Given triangle with sides a = 9, b = 10, c = 13, find all angles accurate to the nearest tenth of a degree.

angle A=43.7°

angle B=50.1°

angle C=86.2°

500

Two ships leave a port at the same time. Ship A travels at 20 knots (nautical miles/hr) on a bearing of N 20° E. Ship B travels at 15 knots (nautical miles/hr) on a bearing of S 40° E. What is the distance between the ships after 2 hours?

10sqrt37 nautical miles or 60.8 nautical miles

Characteristics of Trig Graphs

100

State the amplitude and period of y=3sin⁡(2x).

Amp: 3, Period: pi

200

Describe how the graph of y=cos⁡(1/2x) differs from the graph of y=cos⁡x in period and frequency.

cos(1/2x) has period 4pi so it has fewer cycles in the same amount of radians

300

For y=2sin⁡(3(x−pi/18)+1, state the amplitude, period, phase shift, and midline.

Amp:2, Period: 2pi/3, Phase Shift: pi/18 to the right, Midline: y=1

400

Sketch the graph of the inverse function y=arcsin⁡(x), including necessary domain restrictions.

See the teacher's answer sheet!

500

Given f(x)=Asin⁡(Bx+C)+D, write the equation for the following characteristics: amplitude 4, period pi, phase shift to the right by pi/6, and midline y=−2.

y = 4sin(2(x-pi/6)) - 2

Evaluating Trig Functions/ Compositions

100

Evaluate sin⁡(pi/6) using the unit circle.

1/2

200

Use the unit circle to evaluate tan⁡(3pi/4).

-1

300

Find the exact values of sin⁡θ if the terminal side of θ lies in quadrant III and tan⁡θ=4/3.

sinθ=-4/5

400

Evaluate cos(arccos(1/2)).

1/2

500

Evaluate arctan(sin(pi)).

0