Question

Let (-8,3) be a point on the terminal side of theta. Find the exact values of cos theta, csc theta, and tan theta

Answer 1

Start by drawing a right triangle with legs matching the given point.
Horizontal leg = -8, Vertical leg = 3
The hypotenuse should be identical to a line going from given point to origin.

Next, use pythagorean theorem to find length of hypotenuse.
= sqrt((-8)^2 + 3^2) = sqrt(64+9) = sqrt(73)

Finally use trig ratios for cos, csc, and tan. (csc = 1/sin)
SOH --> sin = opp/hyp = 3/sqrt(73)
csc = 1/sin = sqrt(73)/3

CAH---> cos = adj/hyp = -8/sqrt(73) = (-8*sqrt(73))/73

TOA ---> tan = opp/adj = -3/8