Evaluating Trigonometric Functions
Given an angle, θ, in standard position, where θ > 90◦or θ < 0◦, the referece angle, θ′, is
the acute angle formed by the terminal side of θand the horizontal axis.
Use the following to find the reference angle, θ′:
•If θlies in quadrant II:
·θ′=π−θ
·θ′= 180◦−θ
•If θlies in quadrant III:
·θ′=θ−π
·θ′=θ−180◦
•If θlies in quadrant IV:
·θ′= 2π−θ
·θ′= 360◦−θ
The following is a table of trigonometric values of common angles which will be useful.
θ(degrees) 0◦30◦45◦60◦90◦180◦270◦
θ(radians) 0 π
6
π
4
π
3
π
2π3π
2
sin θ01
2
√2
2
√3
21 0 −1
cos θ1√3
2
√2
2
1
20−1 0
tan θ0√3
31√3 Undef. 0 Undef.
Problem 2.
