IB Mathematics SL/Circular Functions and Trigonometry
Topic 3: Circular Functions and Trigonometry
"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
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)
Double Angle Formulae
cos2(θ)= cos^2(θ)-sin^2(θ)= 2cos^2(θ)-1=1-2sin^2(θ)
Area of a triangle = (1/2) ab sin C