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 lineN

S

EW

35° S 35°E

80°

N 80° W

Harmonic Motion

Assumes ideal conditions; perfect elasticity, no friction, no air resistance, and uniform motion

Equilibrium

Max negativedisplacement

Max positive 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)