Solve the Problem $y = 9 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )$

question 62

Multiple Choice

Solve the problem.
-A vibrating wire has a vertical displacement given by $y = 9 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )$ . Assume $b$ and $t$ are constants. Write $y$ as a cosine function of $x$ .

• A) \(\mathrm { y } = \cos ( 2 \pi \mathrm { x } - \mathrm { bt } )\)
• B) \(y = 9 \cos ( 2 \pi x + b t )\)
• C) \(y = 9 \cos ( 2 \pi x - b t )\)
• D) \(y = 18 \cos ( 2 \pi x + b t )\)

---

Definitions:

Universal Generalization

A logical operation that infers a general statement from specific cases, asserting that a property or relation holds for all members of a certain category.

Universal Instantiation

A logical rule that infers from the truth of a universally quantified statement about all members of a domain, the truth of that statement about any specific member.

Quantifier Negation

The process of applying negation to a statement that contains a quantifier, altering its scope and possibly changing the quantifier type (for example, from universal to existential).

Existential Generalization

A logical operation that infers the existence of at least one object in a domain that satisfies a given proposition.