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Type: Multiple-Choice
Category: Trigonometry
Level: Grade 11
Standards: HSF-TF.A.4
Author: nsharp1
Created: 4 years ago

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Trigonometry Question

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The following questions will investigate the period of the sine, cosine, and tangent functions. The definition of a periodic function is that, for some constant

$T!=0$ ,

$f(x+T)=f(x)$ for all

$x$ in the domain of

$f$ .

For the following questions, let

$theta$ be an angle in standard position. Let the intersection of the terminal arm of

$theta$ and the unit circle centered at the origin be

$(a,b)$ .

Grade 11 Trigonometry CCSS: HSF-TF.A.4

Since the sine function is periodic, we know from the definition of periodic functions that

$sin(theta + T) = sin(theta)$ for some value

$T!=0$ . Since this must be true for all values of

$theta$ , one can look at the specific value

$theta=0$ . Then

$sin(T) = sin(0) = 0$ . Using the unit circle, what values of

$T$ , other than zero, satisfy this equation?

Any integer multiple of $pi/2$ .
Any integer multiple of $pi$ .
Any integer multiple of $2pi$ .
The values $pi$ and $2pi$ .