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)
Double Angle Formulae[edit | edit source]
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