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

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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(39625)   (Show Source): You can put this solution on YOUR website!
Identity, double angle:
Use also the identity which gives you .

sine is for , you want as the double angle,
----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 , this is an angle of about 22 degrees. is still in the first quadrant.
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