Download Reference Angles

January 27, 2015
Reference Angles
The positive acute angle that the terminal
side makes with the x-axis.
To find an angle's reference angle, ask the
question, how far is this angle from the
closest x-axis?
The answer will always be positive and acute.
Quadrantal angles do not have reference
angles. Why not?
Evaluate exactly by using a reference angle.
cos 120º
Step 1: What quadrant is this angle in?
Step 2: Is the value of the given trig function (cos, in this case)
positive or negative in this quadrant from step 1?
Example 5
Find the reference angle for each angle given.
a) 210º
b) 135º
c) 422º
a) sin 315º
Step 4: What is the value of the given trig function (cos, in this case)
for the reference angle?
c) sec (-135º)
Find all possible values of θ where 0º < θ ≤ 360º when each of the
following is true.
a) sin θ = √3 /2
b) cos θ = -½
e) csc (-210º)
f) cos 420º
d) tan 495º
Example 8
Evaluate the trigonometric expressions with a calculator. Round your
answer to four decimal places.
a) cos 317º
b) tan 622º
c) sec (-222º)
d) csc 211º
c) sin θ = 0
e) cot (-82º)
d) cos θ = -1
f) 600º
Example 6
b) sin (-135º)
Example 7
e) 285º
Evaluate the following expressions exactly by using a reference angle
(use the 5 steps we just went through).
Step 3: What is the given angle's reference angle?
Step 5: Combine your sign from step 2 and the numeric value from
step 4 and that's your answer!
d) 160º
January 27, 2015
Example 9
Find the smallest possible positive measure of θ (rounded to the nearest
degree) if the indicated information is true.
a) cos θ = 0.7071 and the terminal side of θ lies in quadrant IV
Example 9 - cont
on your own
Find the smallest possible positive measure of θ (rounded to the nearest
degree) if the indicated information is true.
c) cos θ = -0.3420 and the terminal side of θ lies in quadrant III
d) tan θ = 11.4301 and the terminal side of θ lies in quadrant III
b) sin θ = -0.1746 and the terminal side of θ lies in quadrant III
e) sin θ = -0.4226 and the terminal side of θ lies in quadrant III