A point​ P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions.

Question

A point​ P(x,y) is shown on the unit circle corresponding to a real number t. Find the values of the trigonometric functions.

( -1/5, 2sqrt6/5 )

Answer 1

We are told this point is on the Unit Circle, meaning the radius of the circle is 1 unit. (You can verify this if you want by using the Pythagorean Theorem to calculate the hypotenuse (or radius) like this: (-1/5)² + (2√6/5)² and the result does show the answer is 1.)

So we can draw a picture like this:

So we use that triangle to determine the trig ratios.

sin(θ) = opp/hyp = (2√6/5)/1 = 2√6/5

cos(θ) = adj/hyp = (-1/5)/1 = -1/5

tan(θ) = opp/adj = (2√6/5)/(-1/5) = -2√6

csc(θ) = hyp/opp

sec(θ) = hyp/adj

cot(θ) = adj/opp

(I'll let you figure out those last 3.