SOLUTION: HELLO I am having troubles with the following: if cos(theta) = -1/3 and theta is in quadrant 3. Evaluate sin2(theta) I do not know where to start. thank you much.

Algebra ->  Trigonometry-basics -> SOLUTION: HELLO I am having troubles with the following: if cos(theta) = -1/3 and theta is in quadrant 3. Evaluate sin2(theta) I do not know where to start. thank you much.      Log On


   

Question 645341: HELLO
I am having troubles with the following:
if cos(theta) = -1/3 and theta is in quadrant 3. Evaluate sin2(theta)
I do not know where to start.
thank you much.
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
if cos(theta) = -1/3 and theta is in quadrant 3. Evaluate sin2(theta)
use x for theta
given cosx=-1/3=adj side/hypotenuse
opp side =-√[(hypotenuse^2)-(adj side^2)]=-√(9-1)=-√8
sinx=-√8/3
sin(2x)=2sinxcosx=2*-√8/3*-1/3=2√8/9=4√2/9