Radian measure and its applications Flashcards
What is a radian defined as?
The angle subtended at the centre of a circle by an arc whose length is equal to the circle’s radius
How is an angle of θ radians notated?
θᶜ
How many degrees are in 1ᶜ?
180/π
How many radians are in a complete revolution?
2π
What is the relationship between a circle’s arc length (l), the radius of the circle (r), and the subtended angle, in radians, at the centre of the circle (θ)?
l=rθ
What is the relationship between the area of a sector of a circle (A), the radius of the circle (r), and the central angle, in radians (θ)?
A=r²θ/2
What is the relationship between the area of a segment of a circle (A), the radius of the circle (r), and the angle, in radians, subtended at the centre of the circle (θ)?
A=r²(θ-sin(θ))/2