SOLUTION: If sinθ=3/8 and θ is in the first quadrant, what is sin2θ. Include a diagram Please help as my friends and I have been stumped on this one. I know that for the di

Algebra ->  Trigonometry-basics -> SOLUTION: If sinθ=3/8 and θ is in the first quadrant, what is sin2θ. Include a diagram Please help as my friends and I have been stumped on this one. I know that for the di      Log On


   

Question 867967: If sinθ=3/8 and θ is in the first quadrant, what is sin2θ. Include a diagram
Please help as my friends and I have been stumped on this one. I know that for the diagram, the missing side is simply:
8^2-3^2=x^2
64-9= x^2
55= x^2
Sqrt55=x
7.4162=x
We've also tried using double angle Identity and got as far as:
sin(2x)=2(3/8)cosx
sin(2x)=2(3/8)(7.1462/8)
sin(2x)=2(3)(7.1562)/64
before realizing we might be wrong.
Also please help with the diagramming as well if you can, since we're also trying to figure out if the numbers from sinθ double in it. (i.e. hypotenuse times 2, etc)
Thanks!
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
Identity, double angle: sine%282%2Atheta%29=2%2Asin%28theta%29cos%28theta%29
Use also the identity cos%5E2%28theta%29%2Bsin%5E2%28theta%29=1 which gives you cos%28theta%29=sqrt%281-sin%5E2%28theta%29%29.

sine is 3%2F8 for theta, you want as the double angle, sin%282%2Atheta%29=2%283%2F8%29%2Acos%28theta%29
highlight%28sin%282%2Atheta%29=2%283%2F8%29%2Asqrt%281-%283%2F8%29%5E2%29%29----only needing computation to finish into final value simplified.

Decimal approximation, 0.695, but I suggest working through into simplest radical form, FIRST.


Note that for sin%28theta%29=3%2F8, this is an angle of about 22 degrees. 2%2Atheta is still in the first quadrant.