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3 January, 16:11

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

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  1. 3 January, 17:18
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    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
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