Question

Express f(x) = 3 cos x + 5 sin x as Rsin(x + o), where eis an acute angle in radians.​

Answer 1

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

$e = tan^{-1}\frac{b}{a}$

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

$e = tan^{-1} \frac{5}{3} \\e = 59.09^{0}$

in radians;

$e =\frac{\pi }{180}*59.09\\ e = 0.33\pi rad$

3 cos x + 5 sin x = √34sin(x + 0.33π)