Question

PLZ HELP SO CONFUSED!...Find a possible solution to the equation sin(3x + 13) = cos(4x)

Answer 1

Look at your unit circle and find an angle where the sine and cosine coordinates are the same

Answer 2

~ \(\large\color{black}{ \displaystyle \sin(a+b)=\cos(a)\sin(b)+\sin(a)\cos(b) }\)
~ \(\large\color{black}{ \displaystyle \cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b) }\)

these are the 2 rules u need to apply.

Answer 3

for cosine rule, in your particular case, this is the thing:

\(\large\color{black}{ \displaystyle \cos(4x)=\cos(2x+2x) =\cos(2x)\cos(2x)-\sin(2x)\sin(2x) }\)

\(\large\color{black}{ \displaystyle \cos(4x)=\cos^2(2x)-\sin^2(2x) }\)

Answer 4

so just basically "unfold" everything to an angle of a single x, and solve.

Answer 5

rw-write in terms of sin(x) and cos(x) basically.

Answer 6

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.