From Circle to Sine and Cosine Curves with Angle in Degrees

​
angle (radians)
1
<->
0
π
2
π
3π
2
2π
At the top left the angle
θ
varies from
0
to
2π
. The distances from the origin to the black and blue points are the values of the sine and cosine, respectively. The cosine is plotted with the sine on the right, using a blue isosceles triangle to project the line segment from horizontal to vertical.
The values of
sin(θ)
and
cos(θ)
are shown at the top of the plot.
The lower left circle, which has the same radius as the circle above, shows the right-angled triangle with two sides corresponding to the sine and cosine and its hypotenuse opposite to the right angle.
Inside the lower right circle, the angle
θ
is shown in degrees.

Details

The screen shots show the five presets:
0
,
π
2
,
π
,
3π
2
,
2π
.
They convert sine to cosine (by adding
π
2
) or invert both (by adding
π
).
No triangle is visible in the lower left circle with the presets: the values of sine (
0
,
π
,
2π
) or cosine (
π
2
,
3π
2
) are
0
when angles that are multiples of
π
2
are chosen.

External Links

Cosine (Wolfram MathWorld)
Sine (Wolfram MathWorld)

Permanent Citation

Arthur Stammet
​
​"From Circle to Sine and Cosine Curves with Angle in Degrees"​
​http://demonstrations.wolfram.com/FromCircleToSineAndCosineCurvesWithAngleInDegrees/​
​Wolfram Demonstrations Project​
​Published: March 7, 2011