The unit circle is a fundamental concept in trigonometry and mathematics in general. It is a circle with a radius of 1, centered at the origin of a coordinate plane (0, 0).
Equation: The equation of the unit circle is:x2+y2=1
This means that any point (x,y) on the unit circle satisfies this equation.
Coordinates on the Unit Circle: Any point on the unit circle can be described using an angle, θ\thetaθ, measured from the positive x-axis (counterclockwise for positive angles and clockwise for negative angles). The coordinates of a point on the unit circle corresponding to an angle θ\thetaθ are given by:
(x,y)=(cos(θ),sin(θ))
x-coordinate: cos(θ)
y-coordinate: sin(θ)
Angle Measurement:
Angles on the unit circle are usually measured in radians, though they can also be measured in degrees.
0∘ (or 000 radians) is at the point (1,0)(1, 0)(1,0) on the unit circle.
90∘ (or π2\ radians) is at the point (0,1)(0, 1)(0,1).