5.3.1: Resources and Key Concepts — Read

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Resources

Phase Shift: The horizontal shift of a trigonometric function. It represents the x-value to which the starting point of the principal cycle (originally at \(x=0\)) has been moved.
Midline: A horizontal line that represents the average value of a trigonometric function. For sinusoidal functions, it is the line situated halfway between the maximum and minimum points.

Lemma: Phase Shift Formula for y = trig(x + C): The phase shift for a trigonometric function of the form \(y = \text{trig}(x+C)\) is \(-C\).
Phase Shift Formula: The phase shift of the function \(y = A\text{trig}(Bx+C)\) is \(-\frac{C}{B}\).
Cofunction Identities (radians): The trigonometric function of an angle is equal to the cofunction evaluated at the complement of the angle. For example, \(\sin(\theta) = \cos(\frac{\pi}{2} - \theta)\).

Confusing C with the Phase Shift: In the function \(y = A\text{trig}(Bx+C)\), the phase shift is \(-\frac{C}{B}\), not simply \(-C\). The value of \(B\) affects the horizontal shift.
Ignoring Negative B-values: Before determining the period or phase shift, if the parameter \(B\) is negative, you must first use the Symmetry Identities to make the coefficient of \(x\) positive. Forgetting this step will result in an incorrect phase shift.
Incorrectly Identifying the Midline: The midline is the average of the maximum and minimum values, not simply the lowest point of the graph. It is the horizontal line the graph oscillates around.

This page titled 5.3.1: Resources and Key Concepts was last modified on Thu, 03 Jul 2025 00:46:34 GMT and is shared under a not declared license and was authored, remixed, and/or curated by Roy Simpson.