The point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the angle.

Question

The point is on the terminal side of an angle in standard position. Find the exact values of the six trigonometric functions of the angle.

(−8, 14)

sin θ	=
cos θ	=
tan θ	=
csc θ	=
sec θ	=
cot θ	=

Answer 1

Given the terminal point we know the following:

adjacent = -8

opposite = 14

hypotenuse can use the Pythagorean Theorem to find.

c²=(-8)²+(14)² = 260 Take the square root of both sides

c=√260 = 2√65

sin θ = 14/2√65 = 7/√65

cos θ = -8/2√65 = -4/√65

tan θ = 14/-8 = -7/4

csc θ = √65/7

sec θ = -√65/4

cot θ = -4/7