Question

If secθ = -6.743, find the two values of θ

between 0° and 360°. Round your answers to one
decimal place.

Answer 1

Θ ≈ 98.5° , 261.5°

Explanation:

using the identity

cosΘ =
`(1)/(sec0)` , then

cosΘ =
`(1)/(-6.743)` ≈ - 0.1483

since cosΘ < 0 then Θ is in 2nd and 3rd quadrants

Θ =
`cos^(-1)` (- 0.1483) ≈ 98.5° ← in 2nd quadrant

related acute angle = 180° - 98.5° = 81.5° , then

Θ = 180° + 81.5° = 261.5° ← in 3rd quadrant