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

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: sin t, cos t, tan t, csc t, sec t, and cot t.

P ( - sqrt3/2, - 1/2)

Answer 1

x = -sqrt(3)/2 and y = -1/2

pythagorean says sqrt(3/4 + 1/4) = 1 for the hypotenuse

sine is (-1/2)/ 1 = -1/2

cosine is - sqrt(3)/2

tangent is (-1/2) * -2/ sqrt(3) = sqrt(3)/3

cosecant is -2

secant is -2*sqrt(3)/2

cotangent is sqrt(3)

since sine and cosine are both negative the angle is in quadrant 3, with a flavor of 30 degrees.

The angle is then 210 = 210/180*pi = 7*pi/6