Precalculus

Question

Find all angles which satisfy the following equation. (Use the parameter k as necessary to represent any integer. Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
sec(θ) = −2

Answer 1

sec θ = 1/cos θ = -2

 

cos θ = -1/2

 

Cosine is negative in the second quadrant and third quadrant.

 

θ = arccos -1/2 

 

The reference angle would be 60 degrees or π/3. In the second quadrant this is 120 degrees or 2Π/3. In the third quadrant, this is 240 degrees or 4Π/3.

 

θ = 2π/3 + 2kπ and θ = 4π/3 + 2kπ where k is an integer.