Answer:
√34sin(x + 0.33π)
Step-by-step explanation:
The general form of the equation acosx + bsinx = Rsin(x + e) where R is the resultant of the constants 'a' and 'b' and e is the angle between them.
R = √a²+b²
[tex]e = tan^{-1}\frac{b}{a}[/tex]
Given the function f(x) = 3 cos x + 5 sin x, comparing with the general equation;
a = 3, b = 5
R = √3²+5²
R = √9+25
R =√34
[tex]e = tan^{-1} \frac{5}{3} \\e = 59.09^{0}[/tex]
in radians;
[tex]e =\frac{\pi }{180}*59.09\\ e = 0.33\pi rad[/tex]
3 cos x + 5 sin x = √34sin(x + 0.33π)
