Question

Find the period of the function.

y = -3 cos x

Answer 1

The period of cosine function is 2π.

That doesn't change unless the variable is multiplied by a number. For example if you had y = -3 cos (2x) or y = -3 cos (½x). In those cases the period is 2π divided by the coefficient of x.
- For y = -3 cos (2x) the period is 2π ÷ 2 = π.
- For y = -3 cos (½x) the period is (2π ÷ ½) = 4π

Answer 2

restating what peachpi said

the general cosine function is

y = A*cos(Bx - C) + D

where

|A| is the amplitude
T = 2pi/B is the period
C/B is the phase shift. Positive means right, negative means left
y = D is the midline

Answer 3

but there is only cos x so would the period still be 2pi then

Answer 4

yes

Answer 5

oh okay thank both of your explanations helped i wrote them down

Answer 6

In your case, B = 1 making the period T = 2pi/B = 2pi/1 = 2pi