If point P is on the terminal side of θ, find all trig functions of θ when P(-2, 4).

Question

The more detail the better, to help me understand. Thank you.

Answer 1

It's in quadrant 2 where sine is positive, cosine is negative, and tangent is negative.

adjacent x=-2 and opposite y = 4 ---> hypotenuse sqrt( 4 + 16) = sqrt(20) = 2*sqrt(5)

sine is 4/(2*sqrt(5)) = 2/sqrt(5) = 2*sqrt(5)/5 = (2/5)*sqrt(5)

cosine is -2/(2*sqrt(5)) = -1/sqrt(5) = -sqrt(5)/5

tangent is 4/-2 = -2

cosecant = 5 / (2* sqrt(5)) = 5 * sqrt(5)/10 = (1/2)*sqrt(5)

secant = -5 / sqrt(5) = -sqrt(5)

contangent = -1/2