SOLUTION: Find the exact value of: sin 2theta if cos theta= -(sqrt5)/3 and 180 degrees< theta < 270 degrees? A.) -1/9 B.) -4(sqrt5)/ 9 C.) 1/9 D.) 4(sqrt5)/ 9

Algebra ->  Trigonometry-basics -> SOLUTION: Find the exact value of: sin 2theta if cos theta= -(sqrt5)/3 and 180 degrees< theta < 270 degrees? A.) -1/9 B.) -4(sqrt5)/ 9 C.) 1/9 D.) 4(sqrt5)/ 9      Log On


   

Question 350607: Find the exact value of: sin 2theta if cos theta= -(sqrt5)/3 and 180 degrees< theta < 270 degrees?
A.) -1/9
B.) -4(sqrt5)/ 9
C.) 1/9
D.) 4(sqrt5)/ 9
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
cos%28theta%29=-sqrt%285%29%2F3
sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1
sin%5E2%28theta%29%2B5%2F9=1
sin%5E2%28theta%29=4%2F9
sin%28theta%29=0+%2B-+2%2F3
Since the restriction on theta is 180+%3C+theta+%3C+270, then
sin%28theta%29=-2%2F3
.
.
.
Use the trig identity,
sin%282%2Atheta%29=2sin%28theta%29cos%28theta%29
sin%282%2Atheta%29=2%28-2%2F3%29%28-sqrt%285%29%2F3%29%29
highlight%28sin%282%2Atheta%29=%284%2F9%29sqrt%285%29%29