# How do you find the exact value of #cos^-1 0#?

##### 2 Answers

see below

#### Explanation:

What is the arc which cosine is zero?: two posibilities

This is assuming that

Think of right-angled triangles

#### Explanation:

The trig ratios are defined as ratios of side lengths of a right-angled triangle.

The question here is: What angle in the right-angled triangle results in the ratio of these two sides being zero? Imagine opening up the angle towards another right angle. The closer it gets to 90 degrees, the longer the hypotenuse becomes in order to get across to the far side of the triangle to meet the remaining side. When it gets to 90 degrees, the side is infinitely long - it never meets the other side of the triangle because it's parallel to it. So

Thus