Finding values of trigonometric functions given information about an angle: Problem type 1

Question

Let (-8,-6) be a point on the terminal side of θ.

Find the exact values of sinθ, cscθ, and cotθ



Answer 1

The coordinate point (-8,-6) gives us a triangle with an adjacent side of 8 and an opposite side of 6. Since both values are negative, this triangle is in Quadrant III.

Abbreviations:

hyp = hypotenuse

adj = adjacent = -8

opp = opposite = -6

We can find the hypotenuse using the Pythagorean formula:

hyp² = adj² + opp²

= 8² + 6²

= 64 + 36

= 100

hypotenuse = √(100) = 10.

We can now solve for sine, cosecant, and cotangent:

sin(θ) = opp/hyp = -6/10 = -3/5 = -0.6

csc(θ) = 1/sin(θ) = -10/6 = -5/3

cot(θ) = adj/opp = -8/-6 = 8/6 = 4/3