what is the period of f(t)=4 cos(t+pi/4)?

Question

i really have a hard time knowing it.

Answer 1

AcosB(x-C) + D

 

A= amplitude

1/B*(period for the base function, usually 2pi)= period

C = phase shift

D = vertical shift

 

Note: the coefficient of x MUST BE 1 (factor if necessary to make it so)

 

EXAMPLE:  3sin(4x - pi) - 4

base function is sin x, which has a period of 2pi

factor a 4 from within the parentheses to achieve a coeff of 1

 

3sin4(x - pi/4) - 4

A    B       C      D

Amplitude = 3

B=4, so Period = 1/4 * 2pi = pi/2   (1/B * period of sin x)

Phase shift: set (x- pi/4) = 0 and solve for x, so Phase shift = pi/4

Vertical shift = -4

 

Answer 2

General equation = A cos(wt + c)

 

where w = 2*pi/T

 

compare general eqn with the one in the question -> w = 1.

 

1 = 2*pi/T

 

T = 2pi is the period.