Question

How do you find the exact value of `arccos (-sqrt3/2)`?

Answer 1

The angle whose cosine is `(-sqrt3/2)` is 150 degrees or `5/6pi`

Explanation:

Draw an equilateral triangle.
Cut it in half .
The angles in this right angle triangle are 30 ,60, 90
If the hypotenuse is length 2 then the shortest side is 1 and from Pythagoras the other side is `sqrt3`
So the angle whose cosine is `sqrt3/2` is 30 degrees.
Now sketch the cosine graph.
From this you can find the angle whose cosine is `(-sqrt3/2)`
Is 150 degrees or `5/6pi`