Let θ be an angle in quadrant IV such that sinθ=−7/8. Find the exact values of secθ and cotθ.

Question

Let θ be an angle in quadrant IV such that sinθ=−7/8.

Find the exact values of secθ and cotθ.

Answer 1

I would start by drawing a triangle in quadrant IV in the Cartesian plane with the hypotenuse labeled 8 and the vertical leg (or the y-leg) labeled - 7.

Doing the Pythagorean theorem to find the length of the horizontal leg (or x-leg) of the triangle would yield:

x² + (-7)² = 8²

x² + 49 = 64

x² = 15

x = √(15)

Now that we have the lengths of all three sides of the triangle, it is fairly straightforward to calculate the sec(θ) as well as cot(θ)

Just remember that sec(θ) = 1/cos(θ) and cot(θ) = cos(θ)/sin(θ)