Quandaries and Queries


I don't understand this probelem or what the Professor wants. please help me to understand

Write sin 3x in terms of sin x

Thank you
College freshman




I don't remember very many of the identities in trigonometry, but two I do remember are

  1. sin(A + B) = sin(A)cos(B) + cos(A)sin(B), and

  2. sin2(A) + cos2(A) = 1
So what I see is that if your professor had said write sin 2x in terms of sin x Then you could use identity 1. above to get sin(2x) = sin(x)cos(x) + cos(x)sin(x) = 2 sin(x)cos(x) This is not quite correct since I have cos(2x) in terms of sin(x) and cos(x). But identity 2. above says that cos(x) = sqrt(1 - sin2(x)) where sqrt is the square root. Thus sin(2x) = 2 sin(x) sqrt(1-sin2(x))

To answer your professor's question about sin(3x) first write

sin(3x) = sin(x + 2x) Now use 1. above to write this in terms of sin(x) and sin(2x). But from what I did above you can write sin(2x) in terms of sin(x).


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