Question

Hello, I need help with all these problems. So, I would like someone can help me

Answer 1

2.
`x = (\pi )/(4) , (3\pi )/(4), (5\pi )/(4), (7\pi )/(4)`

3. -0.28

4. a.
`- (\pi )/(6)`

b.
`(3\pi )/(4)`

Explanation:

2. Given that

`2\sin^(2)x = 1`

⇒
`\sin x = (1)/(√(2) )` or
`\sin x = - (1)/(√(2) )`

Since x belongs to [0,2π).

Therefore,
`x = (\pi )/(4) , (3\pi )/(4), (5\pi )/(4), (7\pi )/(4)` (Answer)

3. Given that,
`\cos \theta = (3)/(5)`

⇒
`\theta = \cos^(-1)((3)/(5)) = 53.13` Degrees

{Since
`\theta` is in first quadrant}

So,
`\cos 2\theta = \cos (2 * 53.13) = -0.28` (Answer)

4. a. Given
`\sin^(-1)(- (1)/(2)) = - (\pi )/(6)`

b.
`\cos^(-1)(- (√(2) )/(2) ) = \cos^(-1)(- (1)/(√(2) ) ) = (3\pi )/(4)` (Answer)