How do you find the exact value of sin(arccos(-2/3))

Evelyn Freeman

Evelyn Freeman

Answered question

2022-10-13

How do you find the exact value of sin ( arccos ( 2 3 ) )?

Answer & Explanation

darkangel5991we

darkangel5991we

Beginner2022-10-14Added 10 answers

First note that θ = arccos ( 2 3 ) is in Q2 since 2 3 < 0
In Q2 sin is positive.
From Pythagoras we have:
cos 2 θ + sin 2 θ = 1
and hence:
sin θ = ± 1 cos 2 θ
In our case we want the positive square root and find:
sin ( arccos ( 2 3 ) ) = 1 ( 2 3 ) 2 = 1 4 9 = 5 9 = 5 3

Do you have a similar question?

Recalculate according to your conditions!

New Questions in College Statistics

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?