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Working with a sinusoidal function

This question concerns the function

y/3 = 3+ 4sin [3x+ pi ]

Where x is measured in radians.

(1) Choose the one option which gives the value of the function when x= pi/2

(2) Choose the one option which gives the period of the function.

Options for questions 1 and 2.

A 1
B. 2
C. 3
D. 4
E. pi/3
F. 2pi/3
G. pi
H. 3pi

Solution Preview

our function is

y/3 = 3+ 4sin [3x+ pi ]

when x=pi/2

We have, 3x + pi = (3pi/2)+pi = 5pi/2 = (2pi + pi/2)

Sin function repeats itself when we add 2pi to it

Hence Sin(2pi + pi/2)= Sin(pi/2) = 1

Substitute this value back to the given function and find the value of y.

y/3 = 3+ 4sin ...

Solution Summary

A thorough answer with all mathematical steps.