Question

The terminal side of θ in standard position contains the point (–4, 3). Find the exact values of the six trigonometric functions of θ. (show all of your work) *

Answer 1

Answer:

When we have a rectangular point (x, y), the angle between the x-axis and a ray that connects the origin with this point is given by:

Tan(θ) = y/x.

Cos(θ) = x/(√(x^2 + y^2))

Sin(θ) = y/(√(x^2 + y^2))

So for the point (-4,3) we have:

x = -4

y = 3

√( (-4)^2 + 3^2) = √(16 + 9) = √25 = 5

Then:

Tan(θ) = 3/-4 = -(3/4)

Sin(θ) = 3/5

Cos(θ) = -4/5

And for the other 3 trigonometric functions (the inverses of the 3 above ones) we have:

Ctg(θ) = 1/Tan(θ) = -4/3

Csc(θ) = 1/Sin(θ) = 5/3

Sec(θ) = 1/Cos(θ) = -4/5