Use the Formula $a \cos B x + b \sin B x = A \cos ( B x - C )$

question 15

Multiple Choice

Use the formula $a \cos B x + b \sin B x = A \cos ( B x - C )$ $\text { where } A = \sqrt { a ^ { 2 } + b ^ { 2 } } \text { and } \tan C = \frac { b } { a } \text { with } - \frac { \pi } { 2 } < C < \frac { \pi } { 2 }$ to determine the amplitude of f (x) . $f ( x ) = 2 \cos 4 x - 2 \sin 4 x$

• A) \(A = 11 \sqrt { 2 }\)
• B) \(A = 9 \sqrt { 2 }\)
• C) \(A = 2 \sqrt { 6 }\)
• D) \(A = 2 \sqrt { 2 }\)
• E) \(A = 2\)

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Definitions:

Circular Pitch

This refers to the distance measured along the circumference of a gear from one tooth to another.

Circular Thickness

A descriptive term possibly related to the material thickness of a circular section or detail, but without a standard definition, it may require clarification.

Chordal Thickness

The measurement of the thickness of a gear tooth along the chord, typically at the pitch circle.

Diametral Pitch

A measure of gear tooth density, defined as the number of teeth per inch of the diameter of the gear pitch circle.