Trig Graphs

Understanding Trig Graphs

• Be familiar with the graph shapes for sin(x), cos(x), and tan(x).
• Remember that the graphs of sin(x) and cos(x) are periodic, repeating every 2π, while the graph of tan(x) repeats every π.
• Note that the amplitude (highest point of the graph) for sin(x) and cos(x) is 1, whereas tan(x) does not have a defined amplitude.
• Understand how changes in the functions’ equations lead to transformations in their corresponding graphs.
  • For instance, sin(x + c) shifts the sine graph c units to the left.
  • sin(cx) changes the period of the sine graph to 2π/c.

Graph Transformations

• Know that changes to the amplitude, frequency, phase shift, and vertical shift of the trigonometric functions result in various transformations of the graphs.
• Understand that multiplying a function by a constant changes its amplitude. For example, 2sin(x) has an amplitude of 2.
• Remember that adding a constant to a function results in a vertical shift. Example: sin(x) + 2 shifts the entire graph upwards by 2 units.
• Be aware that multiplying x by a constant changes the frequency. For example, sin(2x) doubles the frequency.
• Finally, adding a constant to x results in a phase (horizontal) shift. For example, sin(x + π/2) shifts the sine curve π/2 units to the left.

Inverse Trig Functions

• Commit to memory that the inverse trigonometric functions are arcsin(x), arccos(x), and arctan(x).
• Bear in mind that these functions give the angle whose sine, cosine or tangent is a given number.
• Note that arcsin(x) and arccos(x) have ranges between -π/2 and π/2, while arctan(x) has a range between -π and π.
• Remember that due to these restricted ranges, these functions can only return one value, making them true inverses of sin(x), cos(x), and tan(x).