• A reference angle is the smallest positive angle
formed by the terminal side of the angle and the xaxis.
• We can sketch the angle in standard position and
then determine how far it lies from the x-axis.
Sketch the angle, then determine the measure of the
reference angle you would use to evaluate. Then evaluate
using your calculator. Round to 4 decimals. (make sure to
look at units)
1.
cos 235
o
2.
sin  255

Sketch the angle, then determine the measure of the
reference angle you would use to evaluate. Then evaluate
using your calculator. Round to 4 decimals. (make sure to
look at units)
3.
csc 213
o
4.
cot 347.3
Sketch the angle, then determine the measure of the
reference angle you would use to evaluate. Then evaluate
using your calculator. Round to 4 decimals. (make sure to
look at units)
5.
cos 2.46
6.
sin 2.7 
Sketch the angle, then determine the measure of the
reference angle you would use to evaluate. Then evaluate
using your calculator. Round to 4 decimals. (make sure to
look at units)
7.
sec11.6
8.
cot 3.75
When given the value of the trig function, we can find
the angle measure using inverse trig on the
calculator. However, the calculator will always give
you one angle measure and we know that there are
two locations for almost every trig ratio. So, you will
need to use reference angles and the given
information to figure out the actual angle that you
are looking for!
Determine the measure of
o
conditions 0   
nearest tenth.


such that
satisfies the given
o
360 . Give your answer in degrees to the
9 . cos   0.9239; sin   0
10.
sin   0.7716; cos   0
Determine the measure of
o
conditions 0   
nearest tenth.
11.


such that
satisfies the given
o
360 . Give your answer in degrees to the
sin   0.7408; cos   0
12.
cos   0.2538; sin   0
Find the angle  to the nearest tenth of a degree so that
o
o
0    90 .
13.
tan  5.000
14.
sec   1.271

Find
to the nearest tenth of a degree so that is in the given
quadrant.
15.
csc   2.572; Q IV

Find
to the nearest tenth of a degree so that is in the given
quadrant.
16.
sec   1.108; Q III