A special relationship exists between the trigonometric values of an angle and those of its reference angle. This important relationship is illustrated in the next exercise.
Exercise #6: In each of the following, an angle and its reference have been given. Using your calculator, in degree mode, determine the sine and cosine of both the angle and its reference. Round all answers to the nearest hundredth.
(a) $\theta = 110^\circ$ and $\theta_r = 70^\circ$
(b) $\theta = 235^\circ$ and $\theta_r = 55^\circ$
(c) $\theta = 282^\circ$ and $\theta_r = 78^\circ$
Clearly the absolute value of the sine and cosine are the same for an angle and its reference. This fact can be exploited to produce sine and cosine values for angles if they are known for their references.
Exercise #7: Given that $\cos(30^\circ) = \frac{\sqrt{3}}{2}$ and $\sin(30^\circ) = \frac{1}{2}$, determine the following values in exact form.
(a) $\cos(150^\circ)$
(b) $\sin(150^\circ)$
(c) $\cos(210^\circ)$
(d) $\sin(210^\circ)$
(e) $\cos(330^\circ)$
(f) $\sin(330^\circ)$
