If (-16, -9) is the terminal side of angle theta, what is the Cosecant and Tangent?

Question

Use the given point of the terminal side of angle "theta" to find the exact value of each trigonometric function. Using point (-16, -9). Solve for Cosecant and Tangent

Answer 1

When you graph the point you see that it lies in Quadrant III. In QIII, cosecant (csc) is negative and tangent (tan) is positive. If you draw a right triangle with 9 as the side length opposite the angle, ∅, and 16 as the length of the adjacent side you can solve for csc and tangent. Using the Pythagorean Theorem, a² + b² = c², with a = -9 and b = -16, you get c = √337.

sin = opp./hyp. = -9/√337

csc = 1/sin = -(√337)/9

tan = opp./hyp. = (-9)/(-16) = 9/16

Hope this helps!

Answer 2

Using the Pythagorean Theorem, we can find the hypotenuse (h):

h = √[(-9)² + (-16)²]

h = √81 + 256)

h = √337

csc(θ) = hypotenuse/opposite = √337/-9 or -√337/9

tan(θ) = opposite/adjacent = -9/-16 = 9/16