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Common Core Standard HSF-TF.B.5 Questions

Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.★

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Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the period of [math]y = 5csc(pi/2 x - (3pi)/2) + 1?[/math]
  1. [math]pi/2[/math]
  2. [math]4[/math]
  3. [math]3[/math]
  4. [math]1/2[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
Which function's graph has a period of 8 and reaches a maximum height of 1 if at least one full period is graphed?
  1. [math]y=-4cos(pi/4x)-3[/math]
  2. [math]y=-4cos(8x)-3[/math]
  3. [math]y=-4cos(pi/4x)+5[/math]
  4. [math]y=-4cos(8x)+5[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
The following table gives the percentage of the moon illuminated (P.I.) on dates in August and early September for a certain city. Given that the phases of the moon are periodic and can be approximately modeled by a trigonometric function, create a function which describes the data presented in the table. Then, use this function to find what approximate percentage of the moon will be illuminated on December 1. Round the answer to the nearest percent.

[math] \ \ \ \ \ \ \ \ mathbf{"Date"} \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \mathbf{"P.I."} \ \ \ \ \ \ \ [/math][math] \ \ [/math][math] \ \ \ \ \ \ \ \ mathbf{"Date"} \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \mathbf{"P.I."} \ \ \ \ \ \ \ [/math][math] \ \ [/math][math] \ \ \ \ \ \ \ \ mathbf{"Date"} \ \ \ \ \ \ \ \ [/math][math] \ \ \ \ \ \ \ \mathbf{"P.I."} \ \ \ \ \ \ \ [/math]
[math] "Aug 1" [/math][math] 96 [/math][math] [/math][math] "Aug 13"[/math][math]31 [/math][math] [/math][math] "Aug 25" [/math][math]40 [/math]
[math] "Aug 2" [/math][math] 99 [/math][math] [/math][math] "Aug 14" [/math][math] 22 [/math][math] [/math][math] "Aug 26" [/math][math] 50 [/math]
[math] "Aug 3" [/math][math] 100 [/math][math] [/math][math] "Aug 15" [/math][math] 14 [/math][math] [/math][math] "Aug 27" [/math][math] 60 [/math]
[math] "Aug 4" [/math][math] 99 [/math][math] [/math][math] "Aug 16" [/math][math] 8 [/math][math] [/math][math] "Aug 28" [/math][math] 71 [/math]
[math] "Aug 5" [/math][math] 96 [/math][math] [/math][math]"Aug 17" [/math][math] 3 [/math][math] [/math][math] "Aug 29" [/math][math] 80 [/math]
[math] "Aug 6" [/math][math] 91 [/math][math] [/math][math] "Aug 18" [/math][math] 0 [/math][math] [/math][math] "Aug 30" [/math][math] 88 [/math]
[math] "Aug 7" [/math][math] 85 [/math][math] [/math][math] "Aug 19"[/math][math] 0 [/math][math] [/math][math] "Aug 31" [/math][math] 94 [/math]
[math] "Aug 8" [/math][math] 77 [/math][math] [/math][math] "Aug 20" [/math][math] 3 [/math][math] [/math][math] "Sept 1" [/math][math] 96 [/math]
[math] "Aug 9" [/math][math] 69 [/math][math] [/math][math] "Aug 21" [/math][math] 9 [/math][math] [/math][math] "Sept 2" [/math][math] 99 [/math]
[math] "Aug 10" [/math][math] 60 [/math][math] [/math][math] "Aug 22" [/math][math] 16 [/math][math] [/math][math] "Sept 3" [/math][math] 100 [/math]
[math] "Aug 11" [/math][math] 50 [/math][math] [/math][math] "Aug 23" [/math][math] 23 [/math][math] [/math][math] "Sept 4" [/math][math] 99 [/math]
[math] "Aug 12" [/math][math] 41 [/math][math] [/math][math] "Aug 24" [/math][math] 29 [/math][math] [/math][math] "Sept 5" [/math][math] 96 [/math]
  1. 3%
  2. 55%
  3. 84%
  4. 96%
Grade 11 Trigonometry CCSS: HSF-TF.B.5
Choose the function that has a period of [math]3pi[/math], an amplitude of [math]4[/math], and a midline of [math]y = 1[/math].
  1. [math]f(x) = 4sin(2/3 x) + 1[/math]
  2. [math]f(x) = 4sin(3pi x) + 1[/math]
  3. [math]f(x) = 2sin(3pi x) + 2[/math]
  4. [math]f(x) = 2sin(2/3 x) + 2[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the period of [math]f(theta) = tan(3theta - 2) ?[/math]
  1. [math]pi/2[/math]
  2. [math]2/3[/math]
  3. [math]pi/3[/math]
  4. [math](2pi)/3[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the period of [math]f(x) = sin(3 pi x - 4) + 2 ?[/math]
  1. [math]2/3[/math]
  2. [math](2pi)/3[/math]
  3. [math](2pi)/4[/math]
  4. [math](3pi)/4[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the amplitude of [math]f(x) = 1/2 cos(pix-1)+2 ?[/math]
  1. [math]3/2[/math]
  2. [math]1/2[/math]
  3. [math]1[/math]
  4. [math]5/2[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the period of [math]f(theta) = 3/4 cot(1/5 theta - 4/5) + 1/2 ?[/math]
  1. [math](4pi)/5[/math]
  2. [math]pi/4[/math]
  3. [math]pi/5[/math]
  4. [math]5pi[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the amplitude of [math]f(x) = 4cos(pi/4x - pi) -4 ?[/math]
  1. [math]4[/math]
  2. [math]1[/math]
  3. [math]0[/math]
  4. [math]1/4[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the midline of [math]f(x) = 2sin(x/4) + 1?[/math]
  1. [math]y=2[/math]
  2. [math]y=1[/math]
  3. [math]y=3[/math]
  4. [math]y=1/2[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the midline of [math]f(x) = 3cos(2x-1/3)-3 ?[/math]
  1. [math]y=3[/math]
  2. [math]y=0[/math]
  3. [math]y=-3[/math]
  4. [math]y=-1[/math]
Grade 11 Trigonometry CCSS: HSF-BF.B.3, HSF-TF.B.5
State the amplitude of the function [math]y=1/3cos(x-2)[/math].
  1. [math]1/3[/math]
  2. [math]pi[/math]
  3. [math]-2[/math]
  4. [math]-pi[/math]
  5. none of these are correct
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