Properties of Sine Function

1. Properties of Sine Function

2. The function is periodic, meaning that it repeats the pattern shown for both positive and negative x. The domain shown constitutes one cycle of the periodic function and the period on an angular basis is 2 radians. • The sine function is an odd function.

3. A. Graph

4. Domain: all real numbers • Range: [-1 , 1] • Period = 2pi • X intercepts: x = k pi , where k is an integer. • Y intercepts: y = 0 • Maximum points: (pi/2 + 2 k pi , 1) , where k is an integer.

5. Maximum points: (pi/2 + 2 k pi , 1) , where k is an integer. • Minimum points: (3pi/2 + 2 k pi , -1) , where k is an integer. • Symmetry: since sin(-x) = - sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the origon (0 , 0).

6. Intervals of Increase/Decrease: over one period and from 0 to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and (3pi/2 , 2pi), and decreasing on the interval (pi/2 , 3pi/2).

7. Source • http://www.analyzemath.com/trigonometry/properties.html