Sultan Temuruly
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06

Unit Circle

Cosine and sine are not new functions to memorise — they are just the two coordinates of a point going round a circle. Drag it, or press play.

WAVE

θ=45°=π/4

(cos θ, sin θ) =0.707,0.707

THE CIRCLE — DRAG THE POINT
-1.5-1-0.50.511.5-1-0.50.51θcos θ = 0.71sin θ = 0.71
y = sin(x)(0.79, 0.71)
0.511.522.533.544.555.56-1-0.50.51xy

The height of the point on the circle is sin θ, and its horizontal position is cos θ. Press play and watch the blue bar on the left trace out the wave on the right.

θ (degrees)
45°
θ (radians)
0.7854
θ (exact)
π/4
cos θ
0.7071
sin θ
0.7071
tan θ
1
Point
(0.707, 0.707)
Quadrant
I
cos²θ + sin²θ
1

ANGLE