Question

Given that (sec(θ) = √ (13/3) and (θ) is in Quadrant IV, what is (tan(θ))? Do not round.

A. (√ 3/√ 13)
B. (-√ 3/√ 13)
C. (√ 13/3)
D. (-√ 13/3)

Answer 1

The value of tan(θ) is -√3/√13.

Step-by-step explanation:

Since sec(θ) is equal to the reciprocal of cos(θ), we can use the Pythagorean identity to find the value of sin(θ). We know that sec(θ) = √(13/3), which means cos(θ) = 1/√(13/3), and sin(θ) = √(1 - cos²(θ)). Since θ is in Quadrant IV, both the sine and tangent of θ will be negative. Therefore, the value of tan(θ) = -√3/√13 (option B).