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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 [math]T!=0[/math], [math]f(x+T)=f(x)[/math] for all [math]x[/math] in the domain of [math]f[/math].

For the following questions, let [math]theta[/math] be an angle in standard position. Let the intersection of the terminal arm of [math]theta[/math] and the unit circle centered at the origin be [math](a,b)[/math].

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

Since the sine function is periodic, we know from the definition of periodic functions that [math]sin(theta + T) = sin(theta)[/math] for some value [math]T!=0[/math]. Since this must be true for all values of [math]theta[/math], one can look at the specific value [math]theta=0[/math]. Then [math]sin(T) = sin(0) = 0[/math]. Using the unit circle, what values of [math]T[/math], other than zero, satisfy this equation?
  1. Any integer multiple of [math]pi/2[/math].
  2. Any integer multiple of [math]pi[/math].
  3. Any integer multiple of [math]2pi[/math].
  4. The values [math]pi[/math] and [math]2pi[/math].
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