Sine + Cosine Graphs

T

100

The maximum value of y = sin x is ______ and occurs at x = _____

maximum value is 1 at x = pi/2

200

The function y = A sin (wx) has amplitude 3 and period 2, then A = ___ and w = ____

A = 3 and w = pi

300

Write the equation of the sine function that has A = 2, P = pi/2, and vertical shift down 3 

y = 2 sin (4x) - 3

400

If y = sin (-2pi/3 x), what is the period?

P = 3

R

100

What is the amplitude and period of y = -2 sin (pi x)?

A = 2 and P = 2

200

For what numbers x, -pi < x < pi is the graph of y = cos x increasing?

(-pi, 0)

300

For what numbers x, 0 < x < 2pi, does cos x = 0.

x = pi/2 and x = 3pi/2

400

If y = 2 cos (2pi x - 4), find A = ___, P = ___, and phase shift = ___

A = 2, P = 1, p.s. = 2/pi

I

100

True or False: sin x = cos (x - pi/2)

True

200

What is the x-intercept of y = cos x on the interval [0, 2pi]

x = pi/2 and x = 3pi/2

300

If y = -1/2 cos (3/2)x, what is the A = ___ and P = ___

A = 1/2 and P = 4pi/3

400

Write the equation of the cosine function which is reflected about the x-axis and has an amplitude of 1, period of 2pi/3, and phase shift of pi/4.

y = - cos 3(x - pi/4)

G

100

What is the y-intercept of y = 2 sin x - 1

-1

200

The function y = 3 cos (6x) has A = ___ and P = ___

A = 3 and P = pi/3

300

If y = 4 sin (2x), the maximum value occurs at x = ___

x = pi/4

400

The function y = 2 sin (x - 3pi/4) has one complete cycle graphed on the interval [3pi/4, ? ]

11pi/4

O

100

What is the y-intercept of y = sin x

0

200

For the graph of y = A sin (wx - t), the number t/w is called the ______

phase shift

300

What is the largest value of y = sin x

1

400

Write the equation of the sine function where A = 3, P = 3pi, and p.s. = -1/3

y = 3 sin 2/3 (x + 1/3)