Question 915095
Use the given information to find the exact value of each of the following.
a) sin of 2 theta
b)cosine of 2 theta
c) tan of 2 theta
given sin theta = -9/41 (sin theta lies in quadrant III) 
***
Use x for theta
sinx=-9/41(given)
cosx=√(1-sin^2x)=√1-(81/1681))=√(1600/1681)=40/41
..
a)sin2x=2sinxcosx=2*(-9/41)*(40/41)=-720/1681≈0.4283
b)cosine2x=1-2sin^2x=1-2*(-9/41)^2=1-0.0964≈0.9036
c)tan2x=sin2x/cos2x=-(720/1681)/.9036)≈-0.4740
..
Check:
sinx=-9/41
x=167.32˚
2x=334.64˚
..
a)sin2x=sin(334.64˚)=-0.4283 (w/calculator)
as computed:-720/1681≈-0.4283
..
b)cos2x=cos(334.64˚)=0.9036 (w/calculator)
as computed:=1-2*(-9/41)^2≈0.9036
..
c)tan2x=tan(334.64˚)=0.4740 (w/calculator)
as computed:=-(720/1681)/.9036)≈0.4740