Exercise 69 Page 520

Let's draw a unit circle showing cos π3 = 12= 0.5.

If we reflect the right triangle in the y-axis, we can make a second statement. Notice that half a lap in the unit circle is π rad. Therefore, by subtracting the reference angle from π, we get the measure of the reflected triangle's angle. π - π/3 = 2π/3We get the statement cos 2π3= -0.5.

Next, we will reflect the new triangle in the x-axis. This triangle will create an angle on the unit circle that is π3 greater than π. π +π/3 = 4π/3 We get the statement cos 4π3= -0.5.

Finally, we will reflect the triangle in the third quadrant in the y-axis which gives us a third statement. This triangle will have an angle that is π3 less than a full lap around the unit circle, 2π. 2π - π/3=5π/3 We get the statement cos 5π3= 0.5.

Note that these are only a few examples of the values of cosine. We could as well subtract multiples of π3 from π3 instead of adding the multiples. Then, we would obtain values of cosine for different arguments.