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

1 Answer
Oct 6, 2016

Answer:

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#