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13.3a – Evaluate Trig Functions of Degrees
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***Left and down are negative lengths. The
hypotenuse is always positive.
1. Evaluate the six trig functions of , given the terminal point.
13

5
(5, 12)
12
12
sin  = 13
13
csc  = 12
cos  = 5
13
sec  = 13
5
tan  = 12
5
5
cot  = 12
.
c2 = a2 + b2
c2 = 52 + 122
c2 = 169
c = 13
.
1. Evaluate the six trig functions of , given the terminal point.
4 5
4

–8
c2 = a2 + b2
c2 = (-8)2 + (4)2
c2
= 80
c4 5
(–8, 4)
sin  =
cos  =
4
4 5

5
5
csc  =
5
8 2 5
sec  =  5

4 5
2
5
tan  = – 4
8
.
cot  = – 2
2. Sketch the angle. Then find its reference angle.
210°
30°
2. Sketch the angle. Then find its reference angle.
-260°
10°
2. Sketch the angle. Then find its reference angle.
690°
30°
3. Make a sketch of the angle, find its reference angle, then
evaluate the function without a calculator.
sin 120° =
3
2
60°
–1
3
2
3. Make a sketch of the angle, find its reference angle, then
evaluate the function without a calculator.
cos -315°=
2
1
45°
1
2
2
3. Make a sketch of the angle, find its reference angle, then
evaluate the function without a calculator.
1
1
csc 240° =
=
 3 2
sin 240°
.
–1
60°
 3
2
2
2 3

3
3
3. Make a sketch of the angle, find its reference angle, then
evaluate the function without a calculator.
sec 675° =
.
2
1
45°
2
1
=
1
cos 675°
–1
1
2
3. Make a sketch of the angle, find its reference angle, then
evaluate the function without a calculator.
1
1
cot –150 ° =
=
tan -150° 1  3
.
 3
30°
–1
2
3