Question

Sin[θ]= 0.7644
θ=???

Answer 1

Perform algebra to remove the sin from the left side of the equation and leave only theta.

Answer 2

The "opposite" of sine is inverse sine.

Answer 3

\[
\theta = \arcsin(0.7644)
\]This will give you the \[
-\pi/2 \leq \theta \leq \pi/2
\]solution. Then you want the \[
\pi/2 \leq \theta \leq 3\pi/2
\]solution.

Answer 4

@1668168

This equation 'is' the answer - you cannot solve it any further by analytical means.

You need to use a calculator or tables to find theta once you know sin(theta)

on your calculator you will may have an 'inv' button - you need to press 'inv sin'
OR you may have a sin^-1 button - which is the direct way to 'inverse sin'

(make sure you have selected the calculator to work in degrees or radians - whichever is required by your answer...)