Question

How do you use the point (3,6) on the terminal side of the angle to evaluate the six trigonometric functions?

Answer 1

`tan x = y/x = 6/3 = 2`
`cos^2 x = 1/(1 + tan^2 x) = 1/(1 + 4) = 1/5`
`cos x = +- 1/sqrt5`
`sin^2 x = 1 - cos^2 x = 1 - 1/5 = 4/5`
`sin x = +- 2/sqrt5 = +- (2sqrt5)/5`
`cot x = 1/(tan) = 1/2`
`sec x = 1/(cos) = +- sqrt5`
`csc x = 1/(sin) = +- sqrt2/5`

Note. The reason we have 2 opposite values for sin x, and cos x, is
because there are 2 arcs (angles) that have the same tan value.
`x = 63^@43` and `x = 63.43 + 180 = 243^@43`