MYP Extended Mathematics Trigonometric Functions and Rules Key Definitions

The maximum distance from the midline (mean value) to a peak or a trough.

A bearing is an angle measured clockwise from the North direction, usually written using three digits (for example, $135^\circ$).

A formula for any triangle that relates a side length to the other two side lengths and the cosine of the included angle. For triangle $ABC$: $a^{2}=b^{2}+c^{2}-2bc\cos A$ (and similarly for $b$ and $c$).

The number of complete cycles per unit interval. In this course, the coefficient $b$ is often referred to as the frequency, representing the number of cycles in $360^\circ$ (distinct from the physics definition of cycles per unit time).

The horizontal length of one complete cycle of a periodic graph.

A function whose values repeat after a fixed input interval $T$, so $f(x+T) = f(x)$ for all $x$ in its domain. The smallest positive such $T$ is the period.

For any triangle $ABC$, $$\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}$$

Equivalently, $$\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$$