Find the values of the trigonometric functions of t from the given information.

Question

Find the values of the trigonometric functions of t from the given information.

tan t =1/8

terminal point of t is in quadrant III

Answer 1

Draw a right triangle with tan(t) = 1/8. The triangle would opposite side 1 and adjacent side 8, so the hypotenuse is sqrt(1^2 + 8^2) = sqrt(65). Since t is in quadrant III, sin(t) and cos(t) are negative. Reading off from the triangle, sin(t) = -1/sqrt(65), cos(t) = -8/sqrt(65). Then cot(t) = 8, sec(t) = -sqrt(65)/8, and csc(t) = -sqrt(65).