Evaluating Trigonometric Functions
If we have any angle, θ, in standard position with a point (x, y) on the terminal side of θ
and r=px2+y2>0, then use the following definitions to evaluate the six trigonometric
functions:
sin θ=y
rcos θ=x
r
tan θ=y
x, x 6= 0 cot θ=x
y, y 6= 0
sec θ=r
x, x 6= 0 csc θ=r
y, y 6= 0
The following figure shows us the quadrants and will also help us to evaluate the
functions:
Quadrant II Quadrant I
sin θ: + sin θ: +
cos θ:−cos θ: +
tan θ:−tan θ: +
Quadrant III Quadrant IV
sin θ:−sin θ:−
cos θ:−cos θ: +
tan θ: + tan θ:−
Problem 1.
Given the following point, which lies on the terminal side of an angle in
standard position, determine the value of the six trigonometric functions of
the angle, θ.
(3,4)
Solution Step 1:
First, find the value of r.
