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Trigonometry > Tangent and Cotangent Functions
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QuickNotes™  

Tangent and Cotangent Functions

Main definitions and formulas:

  • The amplitude of a sine wave is the vertical distance from the middle of the waves to the peaks (or from the middle to the valleys). In the equations above, it is given by | A| .
  • The period of a sine wave is the horizontal distance for the wave to do one complete cycle from one peak to the next peak. In the equations above, it is given by (2π/B).
  • The phase shift of a sine wave is the horizontal distance the wave is shifted from the traditional starting position. In the equations above, it is given by − (C/B).
  • The vertical shift of a sine wave is the vertical distance that the middle of the wave is shifted from the x-axis. In the equations above, it is given by D.

Example 1:

Identify the amplitude, period, phase shift, and vertical shift of the following function, and graph the function:
3 cos(4x+π ) + 2

Example 2:

Identify the amplitude, period, phase shift, and vertical shift of the following function, and graph the function:
− 2 sin( 2x π

3
)

Example 3:

Find a sine wave with amplitude 2, period 4π , phase shift (π/2), and vertical shift 1. Graph the function.

Example 4:

Identify the amplitude, period, phase shift, and vertical shift of the following function, and graph the function:
4 sin ( 2x+ π

2
) − 1

Example 5:

Find a cosine wave with amplitude 2, period 3π , phase shift (π/2), and vertical shift -2. Graph the function.
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