Inverse functions

Solving a problem where we know how much sine is for an unknown angle means that we are to find the angle. In order to solve these equations we use inverse the trigonometric functions called inverse sine or arcsine.


Find the angle where

$$sin\: \Theta =0.7$$

We solve this by taking the inverse sine on both sides, this is notated either by sin-1 or Arcsin:

$$\Theta =arcsin\: 0.7=44.4^{\circ}$$

The same technique is used on both cosine and tangent and is notated with cos-1 or Arccos and tan-1 or Arctan.

Note that sin-1 is not the same as \(\frac{1}{\sin}\),the same goes for cos-1and tan-1.

Video lesson

Solve the following equation tan Ѳ=0.5