Question

If 4cos° + 3sin° =5 ..find sin° and cos°please anyone​

Answer 1

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.