How do you find all sin6x+sin2x=0 in the interval [0,2pi)?

1 Answer
Feb 10, 2017

0, pi/4, pi/2, (3pi)/4, 2pi

Explanation:

Use trig identity:
sin a + sin b = 2sin ((a +b)/2)cos ((a - b)/2)
In this case -->
f(x) = sin 6x + sin 2x = 2sin (4x).cos (2x) = 0

a. sin 4x = 0
Unit circle gives 3 solutions:
4x = 0 --> x = 0
4x = pi --> x = pi/4
4x = 2pi --> x = (2pi)/4 = pi/2
b. cos 2x = 0
trig unit circle gives 2 solutions:
2x = pi/2 --> x = pi/4
2x = (3pi)/2 --> x = (3pi)/4

All answers for (0, 2pi)
0, pi/4, pi/2, (3pi)/4, 2pi