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Determine if the statement is true or false. |3 \sin 6x| \leq 3 for all x.

Question:

Determine if the statement is true or false.

{eq}|3 \sin 6x| \leq 3 {/eq} for all x.

Trigonometric relationships:

Trigonometric relationships can also be considered as functions of a variable that is the measure of an angle. The amplitude of these functions is the amount between which it varies above and below the x-axis. In the particular case of the exercise the breast function fulfills:

{eq}-1 \, \leq \, \sin x \, \leq \, 1 \,\, \forall \, x \, \in \, R {/eq}

Answer and Explanation:

We can affirm that the function {eq}\sin 6x {/eq} meets the following condition

{eq}-1 \, \leq \, \sin 6x \, \leq \, 1 {/eq}

Then{eq}-3 \, \leq \, 3\sin 6x \, \leq \, 3 {/eq}

The statement{eq}|3 \sin 6x| \leq 3 {/eq} is true


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Linear & Direct Relationships

from Physics: High School

Chapter 1 / Lesson 8
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