Question

Question #f4496

Answer 1

`18^@80; 71^@20; 108^@80; 161^@20`

Explanation:

Replace `cos^2 2x` by `(1 - sin^2 2x)` -->
`4sin^2 2x - 1 + sin^2 2x = sqrt3/2`
`5sin^2 2x = 1 + sqrt3/2 = (2 + sqrt3)/2`
`sin^2 2x = (2 + sqrt3)/10`
`sin 2x = +- sqrt(2 + sqrt3)/sqrt10 = +- 0.61`
a. sin 2x = 0.61 -->calculator and unit circle --> 2 solution arcs -->
`2x = 37^@60 --> x = 18^@80`
`2x = 180 - 37.60 = 142^@40 --> x = 71^@20`
b. sin 2x = -0.61 --> unit circle --> 2 solution arcs -->
2x = - 37.60 (or 322.40, co-terminal arc) -->`x = 161^@20`
`2x = 180 + 37.60 = 217^@60 --> x = 108^@80`
Answers for `(0, 2pi)`
`18^@80; 71^@20; 108^@80; 161^@20;`