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lions [1.4K]
2 years ago
8

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

Mathematics
1 answer:
aleksley [76]2 years ago
6 0

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}

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