3.12.1 Drawing trigonometric graph

3.12.1 Drawing trigonometric graph

To draw a trigonometric graph

• Determine the range and period of the function.

  • The range is the set of all possible output values of the function.

  • For trigonometric functions, the range is usually between \( -1 \) and \( 1 \).

• The period is the length of one complete cycle of the function.

  • For trigonometric functions, the period is usually \( 2\pi \).

• Mark the \( x \) axis with tick marks that are evenly spaced apart based on the period of the function.

  • For example, if the period is \( 2\pi \), you might mark the \( x \) axis at intervals of

\( \frac{\pi }{2}, \pi ,\frac{3}{2} \)

• Mark the \( y \) axis with tick marks that are evenly spaced apart based on the range of the function.

  • For example, if the range is between \( -1 \) and \( 1 \), you might mark the \( y \) axis at intervals of \( \frac{1}{2} \).

• Determine the amplitude of the function.

  • The amplitude is the distance from the midline of the graph to the maximum or minimum value of the function.

  • For trigonometric functions, the amplitude is usually \( 1 \).

• Choose a point on the graph to be the starting point.

  • For sine and cosine functions, the starting point is usually \( (0, 0) \).

• Plot points on the graph by evaluating the function at each \( x \) value and then plotting the corresponding point on the graph.

  • For example, if the function is \( y = sin(x) \), you might evaluate the function at \( x = \frac{\pi }{2} \) and plot the point \( (\frac{\pi }{2}, 1) \).

• Connect the points with a smooth curve to complete the graph.