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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]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
Which function's graph has a period of 12 and reaches a maximum height of 7 if at least one full period is graphed?
  1. [math]y=−5cos⁡(12x)+2[/math]
  2. [math]y=−5cos⁡(12x)+12[/math]
  3. [math]y=−5cos⁡((πx)/6)+12[/math]
  4. [math]y=−5cos⁡((πx)/6)+2[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
What is the period of y=2sin⁡([math]π/5[/math]x+3)−1?
  1. 5
  2. 10
  3. [math]π/5[/math]
  4. [math]2π[/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 midline of [math]m(x) = (1/3)cos(πx) + (2/3)[/math] ?
  1. [math]y = 1/3[/math]
  2. [math]y = 2/3[/math]
  3. y = 1
  4. y = 2
Grade 11 Trigonometry CCSS: HSF-TF.B.5
State the amplitude of the function [math]y=−7/4cos⁡(πx−2)[/math].
  1. [math]-7/4[/math]
  2. [math]7/4[/math]
  3. [math]pi[/math]
  4. 2
  5. none of these are correct
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 period of y=2csc⁡[math]((9π)/14x−4)+5[/math].
  1. [math]28/9[/math]
  2. [math](9π)/14[/math]
  3. [math]14/9[/math]
  4. [math](9π)/7[/math]
Grade 11 Trigonometry CCSS: HSF-TF.B.5
State the amplitude of the function y=3.2sin⁡(2x+[math]π/3[/math]).
  1. 2
  2. [math]π/3[/math]
  3. 3.2
  4. 6.4
Grade 11 Trigonometry CCSS: HSF-TF.B.5
State the amplitude of the function [math]y=−2.5sin⁡(0.5x+2)[/math].
  1. -2.5
  2. 2.5
  3. 0.5
  4. 2
  5. none of these are correct
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]
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