TRIGONOMETRY

CIRCULAR MEASURES

ANGLES

DEFINITION ⭐ : An angle measures the amount of rotation between two straight
lines.

EXAMPLES : 🏁

image

image

image

the line OA rotates 60 degree anticlockwise
into position OB. Therefore ΑÔΒ = 60°.

the line OA rotates 150 degree clockwise into
position OC. We measure clockwise rotations with negative
angles.
Th erefore AÔC = −150°

OA can also
move to position OC by rotating 210 degree anti-clockwise, so also
AÔC = 210°,

UNIT

RADIAN & DEGREE

CONVERSION

UNIT CIRCLE

a circle with centre O and radius of 1

image

If point A makes a full rotation around the circle, it will cover a
distance equal to the length of the circumference of the circle.
As the radius of the circle is 1, the length of the circumference
is 2π. Hence a full turn measures 2π radians

one quarter of a full turn, so it measures image
radians.

radians are oft en expressed as
fractions of π but we can also use decimal approximations.

a right angle measures approximately 1.57 radians OR image

TRIANGLE

Full turn = 360° = 2π radians
Half turn = 180° = π radians

To convert from degrees to radians, divide by 180 and
multiply by π.
To convert from radians to degrees, divide by π and
multiply by 180.

CIRCLE PROPERTIES