Question

How do you simplify the following?

arcsin(1/(sqrt2))

Answer 1

We first want to recognize that the SOLUTION to an inverse trig function is an ANGLE.
So we could write it like this,\[\huge \arcsin\left(\frac{1}{\sqrt2}\right)= \theta\]
Recall that the arcsine is the INVERSE of the sine function.
To change it to the sine function, we can swap the arguments like this,\[\huge \sin(\theta)=\frac{1}{\sqrt2}\]

Answer 2

If you don't recognize it as a special angle by now, then try RATIONALIZING the fraction. Meaning, get the irrational number out of the denominator of that fraction. We'll multiply the top and bottom by sqrt2 like so,\[\huge \sin(\theta)=\frac{1}{\sqrt2}\cdot \frac{\sqrt2}{\sqrt2}\]Which will simplify to,\[\huge \sin(\theta)=\frac{\sqrt2}{2}\]This is one of your special angles! :) Do you remember which one?

Answer 3

pi/4

Answer 4

thanks for the help