Why sin and cos are x and y on a unit circle
- Author:
- Nora Teter
This visual explains why the sine ratio and the cosine ratio are the (x, y) coordinates on a unit circle. As you drag point D around the unit circle, you can see how the location of the point (relative to x and y) correlates with the cos and sin values of the angle measurement. Depending on which axis the point is closer to, the value of the cos and sin functions will decrease relative to the axis that it correlates with. If the point is closer to the x axis, the sin will be larger than the cos, if it's closer to the y axis the cos value will be larger than the sin.
For example:
If you start with point D at (0.92,0.4), the cos value (1/.92≈1.0867) is less than than the sin value (1/.4=2.5) because point D is closer to the x axis. Cos correlates with the x axis, so it is the lesser of the values.
If you start with point D at (-0.27,-0.96), the sin value (1/-0.96=.04) is less than the cos value (1/-.27=.73) because point D is closer to the y axis. Sin correlates with the y axis, so it is the lesser of the values.
Cos and sin values can be found under function