TRIGONOMETRY
CIRCULAR MEASURES
ANGLES
DEFINITION ⭐ : An angle measures the amount of rotation between two straight
lines.
EXAMPLES : 🏁
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
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
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
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