Question

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

Answer 1

Answer: sqrt 65/7

Explanation:

I take it you meant θ angle, anyway.

we know the tan(θ) = -4/7... alrite, we also know that 270° < θ < 360°, which is another to say that θ is in the IV quadrant, where the adjacent side or "x" value is positive whilst the opposite side or "y" value is negative.

Answer 2

sec Θ =
`(√(65) )/(7)`

Explanation:

Using the trigonometric identity

sec²Θ = tan²Θ + 1

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

sec Θ > 0, thus

sec²Θ = (-
`(4)/(7)`)² + 1 =
`(16)/(49)` + 1 =
`(65)/(49)`, then

sec Θ =
`\sqrt{(65)/(49) }` =
`(√(65) )/(7)`