Posted by anon on Friday, March 4, 2011 at 6:31am.
theta = 209,55192°
theta = 76,70829°
Sum or difference of sin(θ) and cos(θ) can be solved in the following way, if you are familiar with the sum and difference formulae for sin(a±b).
Given
3sin(θ)-4cos(θ)=2
for a particular φ and amplitude A, we rewrite the above equation as:
Asin(θ-φ)=2
where A=sqrt(3²+4²)=5
or
sin(θ-&phi)=2/5....(1)
=> θ-&phi=asin(2/5)=23.5782°
or 180-23.5782=156.4218°. ...(2)
Expand (1) to get:
sin(θ)cos(&phi)-cos(θ)sin(&phi)=2/5
=> cos(φ)=3/5, sin(φ)=4/5
=> φ=53.1301° or 306.8699°...(3)
So solve for θ from (2) and (3) gives
θ=23.5782+53.1301=76.7083° or θ=156.4218+53.1301=209.5519°
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