Section B.1 Trigonometric Ratio
Table for Trigonometric Ratio
\begin{equation*}
\begin{array}{c|c|c|c|c|c}
Ratio \angle & 0^o & 30^o & 45^o & 60^o & 90^o & 120^o \\ \hline
\sin & 0 & \frac{1}{2} & \frac{1}{\sqrt{2}} & \frac{\sqrt{3}}{2} & 1 & \frac{\sqrt{3}}{2} \\
\cos & 1 & \frac{\sqrt{3}}{2} & \frac{1}{\sqrt{2}} & \frac{1}{2} & 0 & -\frac{1}{2} \\
\tan & 0 & \frac{1}{\sqrt{3}} & 1 & \sqrt{3} & \infty & -\sqrt{3} \\
\end{array}
\end{equation*}
Subsection B.1.1 Co-Function Identity
Co-function Identities Cofunction identities relate trigonometric functions of complementary angles. The ASTC rule All, sine, tan, cos. meaning: In Quadrant 1 All functions are positive. In Quadrant II, Sine function is positive. In Quadrant III, Tangent function is positive. In Quadrant 4, Cosine function is positive.
In Quadrant I & II:
\begin{align*}
\sin(\frac{\pi}{2} \pm \theta) \amp = \cos\theta \\
\cos(\frac{\pi}{2} \pm \theta) \amp = \mp \sin\theta \\
\tan(\frac{\pi}{2}\pm \theta) \amp = \mp \cot\theta
\end{align*}
In Quadrant II & III:
\begin{align*}
\sin(\pi\pm \theta) \amp = \mp \sin\theta \\
\cos(\pi\pm \theta) \amp = -\cos\theta \\
\tan(\pi\pm \theta) \amp = \pm \tan\theta
\end{align*}
In Quadrant III & IV:
\begin{align*}
\sin(\frac{3\pi}{2} \pm \theta) \amp = -\cos\theta \\
\cos(\frac{3\pi}{2}\pm \theta) \amp = \pm \sin\theta \\
\tan(\frac{3\pi}{2}\pm \theta) \amp = \mp \cot\theta
\end{align*}
In Quadrant IV & I:
\begin{align*}
\sin(2\pi \pm \theta) \amp = \pm \sin\theta \\
\cos(2\pi\pm \theta) \amp = \cos\theta \\
\tan(2\pi\pm\theta) \amp = \pm \tan \theta
\end{align*}
