# IB Mathematics SL/Circular Functions and Trigonometry

# Topic 3: Circular Functions and Trigonometry[edit | edit source]

## Introduction[edit | edit source]

"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[edit | edit source]

### Radian Measure[edit | edit source]

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

Degrees = Radians * 180/π

Radians = Degrees * π/180

### Length of an arc[edit | edit source]

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[edit | edit source]

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

## Cosine and Sine (relative to Unit Circle)[edit | edit source]

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

Quadrant | SIN | COS | TAN |
---|---|---|---|

I | + | + | + |

II | + | - | - |

III | - | - | + |

IV | - | + | - |

## Double Angle Formulae[edit | edit source]

sin2(θ)= 2sin(θ)cos(θ)

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

## Triangles[edit | edit source]

### Area[edit | edit source]

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