Question

Write an equation for a sine function and for a cosine function.

sine:
vertical shift - 3
horizontal shift - 0
amplitude - 2
period - 2pi
domain - sin(3x)

cosine:
vertical shift - -3
horizontal shift - 4
amplitude - 2
period - 2pi
domain - cos(2x + 5)

Answer 1

Answer: 1/2

Explanation:

f(x) = A sin (Bx - C) + D

amplitude = |A|

period =

phase shift =

vertical shift = D

A

amplitude of 3 is given so 3 = |A| → A = ± 3, since it is stated that this is a positive function, then A = 3

B

period of 6π is given so

C

D

vertical shift of -1 is given so -1 = D

Now, substitute the values of A, B, C, and D into the formula (above):

Next, solve when x = 2π