SOLUTION: 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

Algebra ->  Trigonometry-basics -> SOLUTION: 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      Log On


   

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)
any help would be really appreciated. Im stuck and having an example to work from could really help
thank you!
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
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