Find the amplitude of the function $2 y = cos (4 (t - 6)) + 6$ $2y=cos (4(t-6))+6$ ?

Question

I know that the simplified form is y=cos(4(t-6))+3
The textbook says that the amplitude is $\frac{1}{2}$ $1/2$ but I don't know how to get to the answer

1327 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-11T21:39:15

See below.

When a trigonometric function is arranged in this form:

$y = a cos (b x + c) + d$ $y =acos(bx +c )+d$

The amplitude is a

The period is $\frac{2 π}{b}$ $(2pi)/b$

Phase shift is $- \frac{c}{b}$ $-c/b$

Vertical shift is $d$ $d$

First rearrange $2 y = cos (4 (t - 6)) + 6$ $2y=cos(4(t-6))+6$

Multiply by $\frac{1}{2}$ $1/2$

$y = \frac{1}{2} cos (4 (t - 6)) + 3$ $y=1/2cos(4(t-6))+3$

Since $a = \frac{1}{2}$ $a=1/2$

The amplitude is $\frac{1}{2}$ $1/2$