SOLUTION: Find the EXACT value. 1. sin (-5pi/12) 2. 2 sin (2 angle)=1 Thanks for the help!

Click here to see ALL problems on Trigonometry-basics

Question 1075418: Find the EXACT value.

1. sin (-5pi/12)
2. 2 sin (2 angle)=1

Thanks for the help!
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
Sin -5pi/12=sin of 19 pi/12 as well.
This is sin (10pi/12+9pi/12)
=sin(10pi/12)*cos(9pi/12)+cos(10pi/12)*sin(9pi/12)
both of these are negative
.5*(-sqrt(2)/2)+(-sqrt(3)/2*sqrt(2)/2)=
sqrt(2)/4+sqrt(6)/4
(1/4)(sqrt(2)+sqrt(6))
-------------------------------
This is sin (2A)=1/2
I know that pi/6 radians gives a sin of 1/2
Therefore, A must be pi/12 radians.
One can check by sin 2A=2sin A cos A =1/2
sinA cos A=1/4
If one uses pi/6 for A or 15 degrees, this will work.
Answer is pi/6 radians.

Answer by ikleyn(52787) (Show Source):
You can put this solution on YOUR website!
.

2. 2*sin(2A) = 1 ----> sin(2A) = ----> 2A = and/or 2A = ----> there are TWO solutions for A: a) A = , and b) A = .