What is \sin(2\arcsin(\frac{3}{5})) ?



Answered question


What is sin(2arcsin(35)) ?

Answer & Explanation



Beginner2022-01-22Added 15 answers

arcsin(35) is some θ between π2 and π2 with sinθ=35
Furthermore, with π2θπ2 and sinθ a positive number, we conclude that θ is between 0 and π2.
We want to find sin2θ and we already know sinθ. So if we find cosθ, then we can ue the double angle formula for sine.
You've probably done this kind of problem many times by now. θ is in the first quadrant and sinθ=35, find cosθ.
Use your favorite method -- draw a triangle, or a unit circle, or an angle in standard position, or skip the picture and use cosθ=±1sin2θ (recall that our θ is in Quadrant 1, so its cosine is positive.)
All of the above is really explanation of our thought process.
All we really need to write is something like:
Let θ=arcsin(35), then sinθ=35 and
And sin(2θ)=2sinθcosθ
So, putting it all together we get:
Jacob Trujillo

Jacob Trujillo

Beginner2022-01-23Added 13 answers

Evaluate arcsin(35).
Multiply 2 by 0.6435011
The result can be shown in multiple forms.
Exact Form:
Decimal Form: 0.96

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