Question

If θ is an angle in standard position and its terminal side passes through the point (7,-4), find the exact value of

sec
⁡
θ
secθ in simplest radical form.

Answer 1

9514 1404 393

Answer:

(√65)/7

Explanation:

We can use the relation between the secant and the tangent:

sec(θ)² = tan(θ)² +1

sec(θ) = √(1 + (-4/7)²) = √(65/49)

sec(θ) = (√65)/7 . . . . . . secant is positive in the 4th quadrant