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

iocasq4 2022-01-21 Answered
What is sin(2arcsin(35)) ?
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Expert Answer

Frauental91
Answered 2022-01-22 Author has 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
cosθ=45
And sin(2θ)=2sinθcosθ
So, putting it all together we get:
sin(2arcsin(35))=2(35)(45)=2425
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Jacob Trujillo
Answered 2022-01-23 Author has 13 answers
Evaluate arcsin(35).
sin(20.6435011)
Multiply 2 by 0.6435011
sin(1.28700221)
The result can be shown in multiple forms.
Exact Form:
sin(2(arcsin(35)))
Decimal Form: 0.96
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