Lesson 57
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This document discusses phase shifts and periods in sinusoidal functions. It notes that shifting a sinusoid left or right does not change its period. It also explains that multiplying the variable of a sinusoid by a constant changes the period inversely by that same constant. The document provides examples showing sinusoidal functions with phase angles and shifted phases, and how to determine coefficients when changing the period between degrees and radians.
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Lesson 57
- 1. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 Period of these sinusoids?
- 2. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 A sinusoid does not have to start at 0 or 1.
- 3. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 1. Write the equation of the sinusoid shown here as a sine curve with a phase angle and also as a cosine curve with a phase angle.
- 4. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 2. Write the equation of this function as a sine curve with a phase shift.
- 5. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 Period of a sinusoid does not change when you shift left or right.
- 6. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 When θ is multiplied by 2 the value of theta changes twice as fast so the period shortens in half. y = sin θ period : 2π y = sin 2θ period : π
- 7. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 To find the coefficient that theta is multiplied we use the following equations. 3600 Coefficient = 2π Coefficient = period in degrees period in radians
- 8. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 3. Write the equation of the curve.
- 9. 57. Phase Shifts and Period in Sinusoids.notebook March 28, 2013 4. Write the equation of the given curve.