If 4cos° + 3sin° =5 ..find sin° and cos°please anyone
1 answer:
Answer:
x = 36.87 degrees.
Step-by-step explanation:
4 cos x + 3 sin x = 5
Use the Auxiliary angle method:
R sin (α + x) = R sin α cos x + R cos α sin x
Comparing coefficients:
R sin α = 4 and R cos α = 3
R sin α / R cos α = 4/3
So tan α = 4/3
α = 53,13 degrees.
Now R^2(sin^2 α + cos^2 α ) = 3^2 + 4^2 = 25
R^2 = 25
R = 5.
R sin (x + 53.13) = 5
5 sin ( x + 53.13) = 5
sin (x + 53.13) = 1
x + 53.13 = 90
x = 36.87 degrees.
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