Question

Select one or more expressions that together represent all solutions to the equation.

Your answer should be in radians.
Assume n is any integer.
30 cos (30x) + 14 = -16
Choose all answers that apply:

Answer 1

D. π/30 + n(π/15)

Explanation:

The given equation can be solved by isolating the cosine function and using the inverse function to find the angles.

Solution

30cos(30x) +14 = -16

30cos(30x) = -30 . . . . . . subtract 14

cos(30x) = -1

This is an extreme value of the cosine function that first occurs where the argument is π, and repeats every 2π after that:

30x = π +2nπ

x = π/30 +n(π/15) . . . . . odd multiples of π/30

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Additional comment

The answer choices other than D include all multiples of π/30, or only even multiples of π/30. Either way, they are not part of the correct answer.