13.2 – define general angles and use radian measure
TRANSCRIPT
13.2 – Define General Angles and Use Radian Measure
0°
90°
180°
270°
Initial side
Terminal side
Standard Position: Vertex at origin and initial side is on x-axis
1. Draw an angle with the given measure in standard position
65°
65°
1. Draw an angle with the given measure in standard position
230°
230°
40°
50°
1. Draw an angle with the given measure in standard position
495°
135°45°
45°
1. Draw an angle with the given measure in standard position
–60°
60°
Radian: Measure of an angle in standard form whose terminal side intercepts an arc of length r
C = 2πr
So there are 2π radians in a circle
Converting Degrees and Radians
degree180
180
radians
Degrees Radians Radians Degrees
2. Convert the degree into radians.
30°
30180
degree180
60
radians6
135°
135180
degree180
4
3radians
4
3
3. Convert the radians into degrees.
180
10
18
180radians
10
18°
5 180
4
45
180radians
5
4
–225°
0
π2
π
3π 2
45°
π4
135°
3π 4
315°225°
5π 4
7π 4
2π
0
π2
π
3π 2
30°
π6
120°5π 6
300°
150°
7π 6
11π 6
60°
π3
2π
2π 3
4π 3
5π 3
330°240°
210°
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
sin 30°
30°
12
3
=1
2
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
cos 45°
45°1
1 2
=1
2
2
2 2
2
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
tan 30° =1
3
3
3 3
3
30°
12
3
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
csc 60° =1
32
60°1
23
1
sin 60
21
3 2 3
3
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
sec 60° =112
60°1
23
1
cos60
211
2
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
cot 45° =111
1
tan 45
111
1
45°1
1 2
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
= 3
2cos
6
6
1 2
3
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
=sin4
4
1
1
2
1
2
2
2 2
2
4. Evaluate the following trigonometric functions without using a calculator. Show work by drawing a triangle for each problem.
=csc3
3
1
23
=1
32
1
sin3
2
3 2 3
3
5. Evaluate the following trigonometric functions with a calculator. Round answers to four decimal places. Remember to change the mode of your calculator.
sin 55° 0.8192
cos 135° – 0.7071
sec 315° 1.4142=1
cos315
cot 76° 0.2493=1
tan 76
5. Evaluate the following trigonometric functions with a calculator. Round answers to four decimal places. Remember to change the mode of your calculator.
0.4816tan7
2.9238csc9
0.58784
sin5
=1
sin9
–22
sec3
=
12
cos3