College Algebra & Trigonometry, 2018a

9.2. GRAPHING TRIGONOMETRIC FUNCTIONS 395
9.2 Graphing Trigonometric Functions
We have seen how to determine the values of trigonometric functions for angles
terminating in Quadrants II, III, and IV. This allows us to make a graph of the
values of the sine function for any angle. In the chart below, I have listed the
values for the sine function for angles between 0 ◦ and 360 ◦ .
θ sin θ θ sin θ
0 ◦ =0 100 ◦ ≈ 0.9848
10 ◦ ≈ 0.1737 110 ◦ ≈ 0.9397
20 ◦ ≈ 0.3420 120 ◦ ≈ 0.8660
30 ◦ =0.5 130 ◦ ≈ 0.7660
40 ◦ ≈ 0.6428 140 ◦ ≈ 0.6428
50 ◦ ≈ 0.7660 150 ◦ =0.5
60 ◦ ≈ 0.8660 160 ◦ ≈ 0.3420
70 ◦ ≈ 0.9397 170 ◦ ≈ 0.1737
80 ◦ ≈ 0.9848 180 ◦ =0
90 ◦ =1
θ sin θ θ sin θ
180 ◦ =0 280 ◦ ≈−0.9848
190 ◦ ≈−0.1737 290 ◦ ≈−0.9397
200 ◦ ≈−0.3420 300 ◦ ≈−0.8660
210 ◦ = −0.5 310 ◦ ≈−0.7660
220 ◦ ≈−0.6428 320 ◦ ≈−0.6428
230 ◦ ≈−0.7660 330 ◦ = −0.5
240 ◦ ≈−0.8660 340 ◦ ≈−0.3420
250 ◦ ≈−0.9397 350 ◦ ≈−0.1737
260 ◦ ≈−0.9848 360 ◦ =0
270 ◦ = −1
On the next page we see a graph of these points plotted on the coordinate axes.