How do i find the exact value of arccos &#x2061;<!-- ⁡ --> ( <mrow class="MJX

Petrovcic2x

Petrovcic2x

Answered question

2022-06-24

How do i find the exact value of
arccos ( 2 3 )
Any ideas on how to find the exact value of the expression without using a calculator?

Answer & Explanation

Cahokiavv

Cahokiavv

Beginner2022-06-25Added 31 answers

How about evaluating in terms of a complex log?
arccos 2 3 = π 2 + i log ( 1 3 + i 2 3 )
Yesenia Sherman

Yesenia Sherman

Beginner2022-06-26Added 5 answers

I think you must have the question wrong. Here is how you would solve it:
Let θ = arccos ( 2 3 ) , so that cos θ = 2 3
What is cos 2 θ?
What is cos 2 θ = 2 cos 2 θ 1?
What is 2 θ?
Step 3 is problematic! I expected cos 2 θ to evaluate to something obvious, like 1 2 or 1 2 or 3 2 But it doesn't. Are you sure about 2 3 ?

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