Determine sinus and cosinus : \(\displaystyle{2}{\sin{{x}}}+{3}{\cos{{x}}}={3}\)

Kason Palmer

Kason Palmer

Answered question

2022-03-28

Determine sinus and cosinus : 2sinx+3cosx=3

Answer & Explanation

kanonickiuoeh

kanonickiuoeh

Beginner2022-03-29Added 8 answers

HINT
You have two equations
2sin(x)+3cos(x)=3
sin(x)2+cos(x)2=1.
Maybe for clarity, replace sin with y and cos with x so you have
2y+3x=3
x2+y2=1
One of these things is a line and one is a circle... find where they intersect. (Further hint: one of these is trivial and one less so.)
This will give the possible values for sin(x) and cos(x) which is what you asked for, but if you want the possible values of x there will be an infinite number corresponding to each of the above solutions due to periodicity.

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