13-4 The Sine Function

Objectives

To identify properties of the sine function

To graph sine curves

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The sine function, y = sin θ , y equals sine theta comma  matches the measure θ of an angle in standard position with the y-coordinate of a point on the unit circle. This point is where the terminal side of the angle intersects the unit circle.

You can graph the sine function in radians or degrees. In this book, you should use radians unless degrees are specified. You can show radian measures along the unit circle as lengths of arcs. In the graphs below, the points for 1, 2, and 3 radians are marked on the unit circle and on the θ-axis.

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Essential Understanding As the terminal side of an angle rotates about the origin (beginning at 0), its sine value on the unit circle increases from 0 to 1, decreases from 1 to − 1 , negative 1 comma  and then increases back to 0.

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