Finding the root mean square of a sum

runddansm88e

runddansm88e

Answered question

2022-04-06

Finding the root mean square of a sum of trig functions
v(t)=32sin(t)+8sin2(t)

Answer & Explanation

regulerenes4w

regulerenes4w

Beginner2022-04-07Added 10 answers

Using
v(t)=32sin(t)+8sin2(t)
and squaring (just brute force), you have (just set x=sin(t) and use binomial expansion)
v2(t)=912sin(t)+52sin2(t)32sin3(t)+64sin4(t)
Now, you can use power reduction formulae which give
sin2(x)=1cos(2x)2
sin3(x)=3sin(x)sin(3x)4
sin4(x)=34cos(2x)+cos(4x)8
Replacing, you the have
v2(t)=5936sin(t)58cos(2t)+8sin(3t)+8cos(4t)

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