Radians, Degrees, The Unit Circle and Solving Trigonometric Equations

Finding Exact Values

100

Give the exact value:

cos (60°)

1/2

200

Give the exact value for:

sin (5π/6)

1/2

300

Give the exact value:

tan(240°)

√3

400

Give the exact value:

cot (-5π/4)

-1

500

Give the exact value:

sec (17π/6)

- (2√3) /3

Law of Sines

100

In triangle ABC, a=4, b=5, and angle A=27°

Find value of angle B

∠B= 34.58°

200

In triangle ABC, angle A=53°, angle C=44°, and c=7ft.

Find the value of a.

a=8ft

300

In triangle XYZ, angle X=13°, angle Y=133° and y=9in. 

Find the value of x.

x=2.77in

400

In triangle ACB, angle C=63°, angle B=101°, and a=9in. 

Find the value of side c.

c=29.1in

500

In triangle ABC, angle B=82°, a=20in, and c=24in.

Find the value of angle A.

∠A= 43.1°

Law of Cosines

100

In triangle ABC, angle C=134°, a=13cm, and b=12cm.

Find the value of c.

c=23cm

200

In triangle ABC, a=6m, b=14m, and c=9m.

Find the value of angle B.

∠B=137°

300

In triangle CBA, angle C=41°, side a=29in, and b=13in.

Find value of side c.

c=21in

400

In triangle BCA, a=10m, b=17m,c=11m. 

Find the value of A.

∠A= 34°

500

In triangle CAB, angle A=88°, b=16.1in, c=21in. 

Find the value of C.

∠C=53.8°

Using y=AsinB(x-C)+D

100

Given the equation y=6sin(x-π/4)+3

What is the Amplitude, Period, Phase Shift, and Vertical Shift?

MUST HAVE ALL CORRECT

Amplitude=6, Period=2π, Phase Shift=π/4, Vertical Shift=3.

200

Given the equation 34.6sin2(x-π/6)-16.7

What is the Frequency?

Frequency= 1/π

300

Given the equation y=6cos4/3(x+π/4)-2

Find the Amplitude, Period, Phase Shift, Vertical Shift, and Frequency.

MUST HAVE ALL CORRECT

Amplitude=6, Period=3π/2, Phase Shift=-π/4, Vertical Shift=-2, Frequency= 2/3π

400

Create an equation using sin for a graph with a amplitude of 5, period of π, slide 1 up, and π/2 right.

y=5sin2(x-π/2)+1

500

Create an equation using cos for a graph with a amplitude of 2, period of 4π, slide 3 down, and π/4 left.

y=2cos1/2(x+π/4)-3

Modeling Electronics & Sound

100

From these three functions,

a(t)=9.8sin(673πt)

b(t)=6.4sin(380πt)

c(t)=8.7sin(1645πt)

Which has the loudest sound?

Which has the lowest pitch?

Loudest sound= a(t)=9.8sin(380πt)

Lowest pitch= b(t)=6.4sin(380πt)

200

From these three functions,

a(t)=10.8sin(543πt)

b(t)=3.8sin(954πt)

c(t)=8.7sin(1812πt)

Which has the softest sound?

Which has the highest pitch?

Softest sound= b(t)=3.8sin(954πt)

Highest pitch= c(t)=8.7sin(1812πt)

300

If the sine wave voltage is given by v=13sin(8280°t) find the peak value, the frequency, and the period of the wave.

Peak value=13, Frequency=23, and Period=1/23

400

If the sine wave is given by h(t)=0.342sin(188πt) find the amplitude, frequency, and period of the wave.

amplitude=0.342, frequency=94, and period=1/94

500

A sound wave is given by f(t)=4.8sin(13680°t), find the amplitude, frequency and the period in milliseconds.

Amplitude=4.8, Frequency=38, Period=26ms