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Common Core Standard HSF-TF.A.3 Questions

(+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π/6, and use the unit circle to express the values of sine, cosine, and tangent for x, π + x, and 2π – x in terms of their values for x, where x is any real number.

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Grade 11 Trigonometry CCSS: HSF-TF.A.3
Find [math]sec(495)[/math].
  1. [math]-sqrt(2) / 2 [/math]
  2. [math]1[/math]
  3. [math]− sqrt2 [/math]
  4. [math]-1[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.3
In triangle ABC [math]tan(B) = sqrt(3)[/math]. What is the length of [math]bar{BC}[/math] if [math]AB = 1/4 \ "unit" ?[/math]
Right Triangle ABC v3
  1. [math]1/8 \ "unit"[/math]
  2. [math]sqrt(3)/12 \ "units"[/math]
  3. [math]4 sqrt(3) \ "units"[/math]
  4. [math]1 \ "unit"[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.3
In triangle ABC, [math]sin(C) = 1/2[/math]. If [math]AC = 6 \ "units"[/math], what is the length of [math]bar{BC} ?[/math]
Right Triangle ABC v2
  1. [math]2 \ "units"[/math]
  2. [math]2sqrt(3) \ "units"[/math]
  3. [math]12 \ "units"[/math]
  4. [math]4sqrt(3) \ "units"[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.3
For triangle ABC, [math]cos(C) = 1/sqrt(2)[/math]. What is the value of [math]BC[/math] if [math]AC = sqrt(3) \ "units"?[/math]
Right Triangle ABC v2
  1. [math]sqrt(2) \ "units"[/math]
  2. [math]sqrt(3)/2 \ "units"[/math]
  3. [math]sqrt(6) \ "units"[/math]
  4. [math]1 \ "unit"[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.3
The side lengths of ΔABC are AB = 2 units, AC = 2√3 units, BC = 4 units. What is the value of cos(B)?
Right Triangle ABC v1
  1. [math]1/2[/math]
  2. [math](√3)/2[/math]
  3. [math]1/(√3)[/math]
  4. [math]√3[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.3
What is the value of tan([math]π/3[/math])?
  1. √3
  2. √2
  3. 1
  4. 0
Grade 11 Trigonometry CCSS: HSF-TF.A.3
What is the value of sin([math]π/4[/math])?
  1. 1
  2. [math]1/2[/math]
  3. [math](√2)/2[/math]
  4. [math](√3)/2[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.3
What is the value of sin([math](11π)/6[/math])?
  1. [math]1/2[/math]
  2. -[math]1/2[/math]
  3. [math](√3)/2[/math]
  4. -[math](√3)/2[/math]
Grade 11 Trigonometry CCSS: HSF-TF.A.3
What is the value of [math]cos((7π)/4)[/math]?
  1. [math]-(√2)/2[/math]
  2. [math](√2)/2[/math]
  3. [math]-1/2[/math]
  4. [math]1/2[/math]
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