anonymous
  • anonymous
PLZ HELP SO CONFUSED!...Find a possible solution to the equation sin(3x + 13) = cos(4x)
Geometry
chestercat
  • chestercat
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anonymous
  • anonymous
Look at your unit circle and find an angle where the sine and cosine coordinates are the same
SolomonZelman
  • SolomonZelman
~ \(\large\color{black}{ \displaystyle \sin(a+b)=\cos(a)\sin(b)+\sin(a)\cos(b) }\) ~ \(\large\color{black}{ \displaystyle \cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b) }\) these are the 2 rules u need to apply.
SolomonZelman
  • SolomonZelman
for cosine rule, in your particular case, this is the thing: \(\large\color{black}{ \displaystyle \cos(4x)=\cos(2x+2x) =\cos(2x)\cos(2x)-\sin(2x)\sin(2x) }\) \(\large\color{black}{ \displaystyle \cos(4x)=\cos^2(2x)-\sin^2(2x) }\)

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SolomonZelman
  • SolomonZelman
so just basically "unfold" everything to an angle of a single x, and solve.
SolomonZelman
  • SolomonZelman
rw-write in terms of sin(x) and cos(x) basically.
freckles
  • freckles
since it says to find A solution I would just say use the co-function identity \[\sin(3x+13)=\sin(\frac{\pi}{2}-4x)\] and set insides equation to find a (one) solution.

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