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CHAPTER 8 KEY FORMULAS AND EQUATIONS

A graph represents diagonal straight line to form right angle triangle with angle, theta and 90. The adjacent is y, hypotenuse as r, and opposite as x. The coordinate is (x, y). — Fig. 1

A unit circle centered at (0, 0) passes through (1, 0), (x, y), (0, 1), (negative 1, 0), and (0, negative 1). Central angle theta has a terminal side with length r = 1 that rises through (x, y). — Fig. 1

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Fig. 1	$\begin{array}{rcl} \sin θ = \frac{y}{r} & \csc θ = \frac{r}{y} \\ \cos θ = \frac{x}{r} & \sec θ = \frac{r}{x} \\ \tan θ = \frac{y}{x} & \cot θ = \frac{x}{y} \end{array}$ (8.1) $trig θ = \pm trig θ_{ref} ("trig" is any trigonometric function)$ (8.2)
Fig. 1	$\begin{array}{l} θ = θ_{ref} & (quadrant I) & θ = 180 ° + θ_{ref} & (quadrant III) \\ θ = 180 ° - θ_{ref} & (quadrant II) & θ = 360 ° - θ_{ref} & (quadrant IV) \end{array}$ (8.3) $\begin{array}{rcl} \sin θ = y & \csc θ = \frac{1}{y} \\ \cos θ = x & \sec θ = \frac{1}{x} \\ \tan θ = \frac{y}{x} & \cot θ = \frac{x}{y} \end{array}$ (8.4)
Negative angles	$\begin{array}{l} \sin (- θ) = - \sin θ & \cos (- θ) = \cos θ & \tan (- θ) = - \tan θ \\ \csc (- θ) = - \csc θ & \sec (- θ) = \sec θ & \cot (- θ) = - \cot θ \end{array}$ (8.5)
Radian-degree conversions	$π rad ...$