Use the given conditions to find the exact value of the expression.

9514 1404 393

  (7 -24√3)/50 = 0.14 -0.48√3

Step-by-step explanation:

Sine is negative and cosine is positive in the 4th quadrant, so ...

  sin(α) = -√(1 -cos(α)²) = -√(1 -576/625) = -7/25

Then the cosine of the angle sum is ...

  cos(α +5π/6) = cos(α)cos(5π/6) -sin(α)sin(5π/6)

  = (24/25)(-√3/2) -(-7/25)(1/2)

  = (7 -24√3)/50 = 0.14 -0.48√3

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step-by-step explanation: