15.4. Graphs of the Other Trigonometric Functions
15.4.1. The Cosine Wave
Try this. Graph at least one cycle of y = sin x. Then on the same axes, graph y = cos x.
How are the two waves similar? How do they differ? How would you obtain one from the other?
15.4.2. Cosine and Sine Curves Related
Note in Fig. 15-19 and in the calculator screen that the cosine curve and the sine curve have the same shape. In fact, the cosine curve appears to be identical to a sine curve shifted 90° to the left, orcos θ = sin(θ + 90°)
We can show that Eq. 1 is true. We lay out the two angles θ and θ + 90° (Fig. 15-20), choose points P and Q so that OP = OQ, and drop perpendiculars PR and QS to the x axis. Since triangles OPR and OQS are congruent, we have OR= QS. The cosine of θ is then
which verifies Eq. 1.
Calculator graphs of y = sin x, shown light, and y = cos x, shown heavy. Tick marks are 30° apart on the x axis and one unit apart on the y axis.