#5 Radians

What are the 2 measures of angles?

Degrees

Radians

What is a radian?

The angle subtended at the centre of the circle by an arc whose length is equal to the radius of the circle

How many degrees are in 2pi radians?

360*

How many degrees are in pi radians?

180*

State how to convert from radians to degrees.

Multiply by 180* / pi

State the formula for arc length using radians.

length = radius x angle

State the formula for sector area using radians.

Area = ½ x radius² x angle

State what is meant by a minor sector?

The smaller sector of the circle subtended by the angle

State how to find the area of a segment.

Subtract the the area of the triangle from the area of the sector

State the formula for calculating the area of a segment.

Area = ½ x radius² x (angle - sin(angle))

State the approximation for sinX and X is very small.

sinX ~ X

State the approximation for tanX and X is very small.

tanX ~ X

State the approximation for cosX when X is very small.

cosX ~ 1 = X² / 2

When approximating small angles, what can be done with larger powers and why?

They can be excluded as they give very small, irrelevant values