Answer:
[tex]\theta = \frac{\pi}{2}[/tex]
Step-by-step explanation:
Given
[tex]\sin(\theta) = 1[/tex]
[tex]0 < \theta < \pi[/tex]
Required
Find [tex]\theta[/tex]
[tex]0 < \theta < \pi[/tex] implies that [tex]\theta[/tex] is between 0 and 180 degrees
[tex]\sin(\theta) = 1[/tex]
Take arcsin of both sides
[tex]\theta = sin^{-1}(1)[/tex]
This gives:
[tex]\theta = \frac{\pi}{2}[/tex]
Convert to degrees
[tex]\theta = \frac{\pi}{2} * \frac{180}{\pi}[/tex]
[tex]\theta = 90[/tex]
We have:
[tex]0 < \theta < \pi[/tex] or [tex]0 < \theta < 180[/tex]
To get other values of [tex]\theta[/tex]
We use:
[tex]\sin(\theta) = \sin(180 - \theta)[/tex]
Substitute: [tex]\theta = 90[/tex]
[tex]\sin(90) = \sin(180 - 90)[/tex]
[tex]\sin(90) = \sin(90)[/tex]
This means that there are no other values of [tex]\theta[/tex] in the given range
