How to evaluate sin ((13pi)/12)?

onteringsdh

onteringsdh

Answered question

2023-02-15

How to evaluate sin ( 13 π 12 ) ?

Answer & Explanation

Marques Cervantes

Marques Cervantes

Beginner2023-02-16Added 3 answers

sin ( 13 π ) 12 = sin ( π 12 + π ) = - sin ( π 12 ) .
Evaluate sin (pi/12) by the trig identity:
cos 2 a = 1 - 2 sin 2 a
Call π 12 ) = t , we get cos ( 2 t ) = cos ( π 6 ) = 3 2
The resulting equation is:
3 2 = 1 - 2 sin 2 t
2 sin 2 t = 1 - 3 2 = 2 - 3 2
sin 2 t = 2 - 3 4
sin t = sin ( π 12 ) = ± 2 - 3 2
Given that sin ( π 12 ) is positive,thus,
sin ( 13 π 12 ) = - sin ( π 12 ) is negative.
Final answer: sin ( 13 π 12 ) = - 2 - 3 2

Do you have a similar question?

Recalculate according to your conditions!

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?