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Sine

The sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle.

The sine ratio is the same regardless of the size of the right triangle. So, it is often easiest to consider a right triangle with a hypotenuse of length 1.

The sine ratio can also be thought of as a function, which takes different values depending on the measure of the angle. You can measure an angle in degrees or radians.

Suppose you have an angle measuring θ radians. Draw a unit circle on the coordinate plane and draw the angle centered at the origin, with one side as the positive x-axis. The y-coordinate of the point where the other side of the angle intersects the circle is sin θ, and the x-coordinate is cos θ.

There are a few sine values that should be memorized, based on 30°-60°-90° triangles and 45°-45°-90° triangles.

Once you know these values, you can derive many other values for the sine function. Remember that sin θ is positive in quadrants I and II and negative in quadrants III and IV.

To read about graphing these values and seeing the graph of y = sin x, click here.

See also: cosine and tangent.