Question

find the missing value? sin =8 over 15. I know the answer 32.23 but what I don't know is how to solve the problem. is there anyone that can explain it to me.

Answer 1

So,
\(\sin(x)=\dfrac8{15}\)
where \(x\) is the missing value?

You can use the arcsine or inverse sine function.
In math, many people write it as \(sin^{-1}\)

The cool thing is that if you take the inverse sine of the whole thing (the equation will still be true), you get \(x\) on the left side.

That's because the inverse sine of a sine of anything is just that anything.
Like, on the left side, we have
\(\sin^{-1}\left(\sin(x)\right)=x\)
It's that simple. In terms of the unit circle, it will find the angle (\(x\)) that gives you the sine function value.

So, you take the inverse sign of both sides to get
\(\sin^{-1}\left(\sin(x)\right)=\sin^{-1}\left(\dfrac8{15}\right)\)
\(=x=32.231....^\circ\approx32.23^\circ\)

A scientific calculator will have an inverse sine button just like it will have a sine button.