Solve sin2(x)=cos(x )for all solutions 0≤x<2π. Ask for X? Give your answers accurate to 2 decimal places, as a list separated by commas

1 Answer
Jun 20, 2018

5183,30817

Explanation:

sin2x=cosx
(1cos2x)=cosx
cos2x+cosx1=0.
Solve this quadratic equation for cos x.
D=d2=b24ac=1+4=5 --> d=±5
There are 2 real roots:
cosx=b2a±d2a=12±52=1±52
a. cosx=152=3.242=1.62 (rejected as < - 1)
b. cosx=1+52=0.62
Calculator and unit circle give 2 solutions for x -->
x=±5183
Note. x = - 51.83 is co-terminal to x=36051.83=30817
Answers for (0,2π)
5183,30817
Check by calculator.
x = 308.17 --> sin2x=0.62 --> cos x = 0.62. Proved