Calculate cos^-1(0)

Step by step

The question

Question: find cos⁻¹(0).

1 What it asks

cos⁻¹ of 0 means: the angle whose cosine is 0.

We call that angle θ.

So cos θ = 0.

2 The allowed range

Many angles have a cosine of 0.

270° and 450° work too.

The cos⁻¹ button must give just one.

So cos⁻¹ only gives angles from 0° to 180°: the top half of the circle.

There, every cosine from −1 to 1 happens just once.

3 Find the angle

Careful!

Other angles have the same cos, like 270°.

But only 90° is in the range.

So the button gives 90°.

90° is in the range.

So θ = 90°.

4 In radians

In radians: 90 times π over 180.

That is π/2.

So cos⁻¹(0) = 90° = π/2.

5 Check

Let's check: cos 90° is 0.

And 90° is inside the range.

So it is right!

Let's look back.

First: what it asks.

Then: the allowed range.

Then: find the angle.

Then: in radians.

Last: check.