Given a right-triangle (a triangle with a right angle) with acute angle α, the sine of α is the value of the ratio: $ \sin(\alpha)=\large{\frac{\text{side opposite}\,\, \alpha}{\text{hypotenuse}}}=\large{\frac{\text{opp}}{\text{hyp}}} $

Click and drag the slider for α. Note the size of α in degrees and in radians. (Although we wrote the word radians, it should NOT be written. There is no unit with radians.)

The ANGLE α is on the x-axis. The ANGLE α is the LENGTH OF THE ARC in the unit circle for the angle α in degrees. Read this sentence until you understand it. It is critical.

The y-coordinate of the point T ((height of the triangle) is the value of the sine function of the angle α.

Definition of Sine Directions and Links

sinkey and the size of the angle α orSine - Nested Triangles Directions and Links

y=sin(x) & Unit Circle - Degrees Directions and Linksy=sin(x) & Unit Circle - Radians Directions and Links