Question

Given that tan theta = -4/7, and 270° < theta < 360°, what is the exact value of sec theta​

Answer 1

Answer:

sec Θ = $\frac{\sqrt{65} }{7}$

Step-by-step explanation:

Using the trigonometric identity

sec²Θ = tan²Θ + 1

Since 270° < Θ < 360° ← that is fourth quadrant, then

sec Θ > 0, thus

sec²Θ = (- $\frac{4}{7}$)² + 1 = $\frac{16}{49}$ + 1 = $\frac{65}{49}$, then

sec Θ = $\sqrt{\frac{65}{49} }$ = $\frac{\sqrt{65} }{7}$