Question

The coordinates of the five quarter points for y=sin(x) are given below.

Use these quarter points to determine the​ y-coordinates of the quarter points of y=5sin(-π/3x).

(0,0)

(π/2,1)

(π,0)

(3π/2,-1)

(2π,0)

(Type ordered pairs. Type exact​ answers, using π as needed)

- Please show steps and answers because I want to learn it.

Answer 1

the period of sin(x) is 2π.
the period of sin(-π/3 x) is 2π/(π/3) = 6

You need to multiply by the amplitude.

You need to reflect in the x-axis, since sin(-x) = -sin(x)

so, the quarter points are
(0,0), (3/2,-5), (3,0), (9/2,5), (6,0)

see the graph at

http://www.wolframalpha.com/input/?i=5sin(-%CF%80%2F3+x)

Answer 2

Y=1/5cos (-5x)