How to evaluate cot (-pi/6)?

Lilia Mccarthy

Lilia Mccarthy

Answered question

2023-03-16

How to evaluate cot ( - π 6 ) ?

Answer & Explanation

coguarsbq2q

coguarsbq2q

Beginner2023-03-17Added 10 answers

The following will be employed:
(1) cot ( x ) = cos ( x ) sin ( x )
(2) sin ( - x ) = - sin ( x )
(3) cos ( - x ) = cos ( x )
(4) cos ( π 6 ) = 3 2
(5) sin ( π 6 ) = 1 2
Verifying these facts is a worthwhile exercise that may be carried out using the unit circle for units 1-3 and some basic definitions.
As a clue, divide an equilateral triangle with side length 1 into two equal right triangles to solve problems 4 and 5. What are the right triangles' angles?
This has given us
cot ( - π 6 ) = cos ( - π 6 ) sin ( - π 6 ) (by 1)
cot ( - π 6 ) = cos ( π 6 ) - sin ( π 6 ) (by 2 and 3)
cot ( - π 6 ) = - 3 2 1 2 = - 3 (by 4 and 5)

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