Question

Circuit Training If sin0 =1 and 0 <0< π find 0.

Answer 1

`\theta = (\pi)/(2)`

Explanation:

Given

`\sin(\theta) = 1`

`0 < \theta < \pi`

Required

Find
`\theta`

`0 < \theta < \pi` implies that
`\theta` is between 0 and 180 degrees

`\sin(\theta) = 1`

Take arcsin of both sides

`\theta = sin^(-1)(1)`

This gives:

`\theta = (\pi)/(2)`

Convert to degrees

`\theta = (\pi)/(2) * (180)/(\pi)`

`\theta = 90`

We have:

`0 < \theta < \pi` or
`0 < \theta < 180`

To get other values of
`\theta`

We use:

`\sin(\theta) = \sin(180 - \theta)`

Substitute:
`\theta = 90`

`\sin(90) = \sin(180 - 90)`

`\sin(90) = \sin(90)`

This means that there are no other values of
`\theta` in the given range