In this animation we plot [math]y=\sin(\alpha)[/math]. Here the label and unit on the [i]horizontal[/i]-axis is [math]\alpha[/math] in degrees. There is no unit on the [i]y[/i]-axis. The [i]y[/i]-value of the sine function for the angle [math]\alpha[/math] is the [i]y[/i]-coordinate of the point T. (Remember: the [i]y[/i]-value of the cosine function for this angle is the [i]x[/i]-coordinate of the point T.)

Move the slider to α=45°. The [math]\sin(45^\circ) \approx 0.707[/math]. Do you know the exact value of [math]\sin(45^\circ)[/math]?[br]Move the slider to α=135°. The [math]\sin(135^\circ) \approx 0.707[/math]. Do you know the exact value of [math]\sin(135^\circ)[/math]?[br]Now, let α=–45°. Move the slider to the corresponding angle between 0° and 360°. The [math]\sin(–45^\circ)=\sin(315^\circ) \approx –0.707[/math]. Do you know the exact value of [math]\sin(–45^\circ)[/math]?[br]Does this agree with the fact that sin(–α)=–sin(α)?