Find the value of six trigonometric functions given P(x,y) is on the terminal side of angle theta, with theta in standard position. (2,8)

Question

Find the value of six trigonometric functions given P(x,y) is on the terminal side of angle theta, with theta in standard position.

1. (2,8)

2.(4radical3,4)

Answer 1

If P(x)=(2,8) then

adjacent = 2

opposite = 8

hypotenuse =√(2²+8²) = √68 = 2√17

Using SOH CAH TOA

sin = 8/2√17 = 4/√17

cos = 2/2√17 = 1/√17

tan = 8/2 = 4

Now for each of these, take the reciprocals.

csc = √17/4

sec = √17

cot = 1/4