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CHAPTER 4 KEY FORMULAS AND EQUATIONS

The terminal side of counterclockwise angle theta passes through (x, y) with length r. The horizontal distance from the origin to (x, y) is x, and the vertical distance is y. A dashed segment from (x, y) meets the x-axis at a right angle.

A right triangle with legs ay and b meeting at a right angle, and hypotenuse c opposite the right angle.

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	$\begin{array}{l} \sin θ = \frac{y}{r} & \csc θ = \frac{r}{y} \\ \cos θ = \frac{x}{r} & \sec θ = \frac{r}{x} \\ \tan θ = \frac{y}{x} & \cot θ = \frac{x}{y} \end{array}$ (4.1)
	Pythagorean theorem $c^{2} = a^{2} + b^{2}$ (4.2)
	$\begin{array}{l} \sin A = \frac{side opposite A}{hypotenuse} & \csc A = \frac{hypotenuse}{side opposite A} \\ \cos A = \frac{side adjacent A}{hypotenuse} & \sec A = \frac{hypotenuse}{side adjacent A} \\ \tan A = \frac{side opposite A}{side adjacent A} & \cot A = \frac{side adjacent A}{side opposite A} \end{array}$ (4.5)