4.8 Applications and Models Real world applications

Solving a right triangle Label the given sides and angles using A, B, C for the angles and a, b, c for the sides. Use trig ratios to solve for all missing sides and angles When given one angle, subtract from 90 to find the third angle

Right triangle applications

Trigonometry and bearings Used in surveying and navigation Bearing- the acute angle a path or line of sight makes with a fixed north-south line N N 80° W 80° E W 35° S 35°E S

Harmonic Motion Assumes ideal conditions; perfect elasticity, no friction, no air resistance, and uniform motion Max positive displacement Equilibrium Max negative displacement

Simple Harmonic Motion The distance d from the origin at a time t d=a sin kt or d=a cos kt Where k and a are real numbers such that k>0. The motion has amplitude |a|, period 2π/k and frequency k/(2π)