APPC Unit 3.1 - 3.5

Periodic Phenomena

100

What does it mean for a phenomenon to be periodic?

cycle repeats regularly

200

When are Boy's Tennis Tryouts?

February 2nd

300

A tide rises and falls twice every 24 hours. What is the period of the tide cycle?

12 hr

400

If a sound wave has a frequency of 5 Hz, what is its period?

 0.2 s

500

A pendulum repeats its motion every 3 seconds. How many complete cycles occur in 1 minute?

 20 cycles

Sine, Cosine, Tangent

100

Find the value of sin(pi/3)

sqrt(3)/2

200

Find the value of cos(-pi/2).

0

300

Given sin(7pi/2), draw the angle in standard position and evaluate sin(7pi/2).

-1

400

Draw the angle and evaluate cos(-11pi/6).

sqrt(3)/2

500

Write an expression that gives all values where tan(theta) is undefined given an integer n.

theta = pi/2 +npi for all integer values of n.

Sin and Cos Values

100

A point is on a circle of radius 1 at angle θ=pi/2. Find the y-coordinate (y=rsin⁡θ).

1

200

A point is on a circle of radius 1 at angle θ=pi/3. Find the x-coordinate (x=rcos⁡θ)).

1/2

300

A point lies on a circle of radius 2 at angle θ=pi/4. Find the coordinates (x,y).

(sqrt2, sqrt2)

400

A point is on a circle of radius 5 at angle θ=7pi/6. Find the coordinates (x,y) and evaluate tan⁡θ.

sqrt(3)/3

500

A point has coordinates ( −6, 6sqrt(3) ) on a circle centered at the origin. Find the radius and the angle θ in radians.

r =sqrt( (-6)^2 + (6sqrt3)^2) = sqrt (36 +108) = 12

tan(theta) = 6sqrt(3) / -6 = -sqrt(3).  theta  = 2pi/3

Sin and Cos Graphs

100

What is the amplitude of y=sin⁡x?

1

200

What is the period of y=cos⁡x?

2pi

300

What is the midline of y=3sin⁡x+2?

2

400

What is the amplitude of y=−4cos⁡x?

4

500

What is the period of y=sin⁡(2x)?

pi

Sinusoidal Functions

100

A Ferris wheel has a maximum height of 90 ft and a minimum height of 30 ft. Find the midline.

60 ft

200

Where did Mari go to high school? (Hint: it's part of this district)

Mt. Pleasant

300

A pendulum completes 15 swings in 30 seconds. Find the period.

2 s

400

The daily temperature ranges from 58°F to 86°F and repeats every 24 hours. Find the amplitude, midline, period, and frequency.

Amplitude = 14°F, Midline = 72°F, Period = 24 hr, Frequency = 1/24 cycles/h

500

A buoy moves between 0.5 m and 2.5 m above sea level and completes 12 cycles in 6 minutes. Find the amplitude, midline, period, and frequency.

Amplitude = 1 m, Midline = 1.5 m, Period = 0.5 min, Frequency = 2 cycles/min