Math Homework. Do It Faster, Learn It Better.

Sine Function

The sine function is a periodic function which is very important in trigonometry.

The simplest way to understand the sine function is to use the unit circle. For a given angle measure θ , 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 .

You can plot these points on a coordinate plane to show part of the sine function, the part between 0 and 2 π .

For values of θ less than 0 or greater than 2 π you can find the value of sin ( θ ) using the reference angle .

The graph of the function over a wider interval is shown below.

Note that the domain of the function is the whole real line, while the range is 1 y 1 .

The period of f ( x ) = sin ( x ) is 2 π . That is, the shape of the curve repeats every 2 π -