Question

Solve for x on the domain 0 < x < 12:
cos x= -0.814

Answer 1

Replace 10.0 with 10.04

Explanation:

`\cos(x) = - 0.814`

`\cos {}^( - 1) ( - 0.814) = x`

`x = 2.52`

Next, use the identity

`\cos(x) = \cos(2\pi - x)`

`\cos(2.52) = \cos(2\pi - 2.52)`

`\cos(2.52) = \cos(6.28 - 2.52)`

`\cos(2.52) = \cos(3.76)`

So another solution is 3.76

After that, use the identity

`\cos(x + 2\pi) = \cos(x)`

So use that for 2.52 and 3.76

`\cos(2.52 + 2\pi) = \cos(8.80)`

8.80 is one solutiin

`\cos(3.76 + 2\pi) = \cos(10.04)`