Question

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

Assume n is any integer.
30cos (30x)+14=-16
Choose all answers that apply:
A. -π +n· 2π
B. n· π /30
C. n· π /15
D. π /30 +n· π /15
E. π +n· π /30

Answer 1

To find the solutions to the equation 30cos (30x)+14=-16, we can use the cosine values for special angles and their multiples. The expressions that represent all solutions are -π +n· 2π, n· π /15, and π +n· π /30.

Step-by-step explanation:

To find the solutions to the equation 30cos (30x)+14=-16, we can start by isolating the cosine term.

Subtracting 14 from both sides of the equation gives us 30cos (30x)=-30.

Then, we divide both sides by 30 to get cos (30x)=-1.

Next, we can recall the cosine values for special angles and their multiples to find the solutions.

the expressions that represent all solutions are A. -π +n· 2π, C. n· π /15, and E. π +n· π /30.