Trigonometry: If f (x) = 2sinx + cosx using exact values find f (120 degrees). if possible show steps.

Answer: f (120°) = (√3) + 1/2

Step-by-step explanation:

i will solve it with notable relations, because using a calculator is cutting steps.

f (120°) = 2*sin (120°) + cos (120°)

=2*sin (90° + 30°) + cos (90° + 30°)

here we can use the relations

cos (a + b) = cos (a) * cos (b) - sin (a) * sin (b)

sin (a + b) = cos (a) * sin (b) + cos (b) * sin (a)

then we have

f (120°) = 2 * (cos (90°) * sin (30°) + cos (30°) * sin (90°)) + cos (90°) * cos (30°) - sin (90°) * sin (30°)

and

cos (90°) = 0

sin (90°) = 1

cos (30°) = (√3) / 2

sin (30°) = 1/2

We replace those values in the equation and get:

f (120°) = 2 * (0 + (√3) / 2) + 0 + 1/2 = (√3) + 1/2