# Topic 3: Circular Functions and Trigonometry

## Introduction

"The aims of this topic are to explore the circular functions and to solve problems using trigonometry. On examination papers, radian measure should be assumed unless otherwise indicated."

- From IB Math SL Guide

## Circle

There are 2π radians in a complete circle, and π radians in a half circle. Therefore as there are 360 degrees in a complete circle, and 180 degrees in a half circle, we can derive this equation to convert

### Length of an arc

The length of an arc is equal to s=r(θ), where r= radius, (θ)=inscribed angle in radians, and s=the length of the arc.

This formula is synonymous with the formula for the circumference of a circle where (theta)=2(pi).

### Area of a Sector

A = (1/2)(θ)(r^2) where r is the radius.

## Cosine and Sine (relative to Unit Circle)

sinθ=y cosθ=x tanθ=y/x CAST Beginning from the IV section will let you know which are positive (Cosine, All, Sine, Tangent)

I + + +
II + - -
III - - +
IV - + -

## Double Angle Formulae

sin2(θ)= 2sin(θ)cos(θ)

cos2(θ)= cos^2(θ)-sin^2(θ)= 2cos^2(θ)-1=1-2sin^2(θ)

## Triangles

### Area

Area of a triangle = (1/2) ab sin C