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Common Core Standard HSF-TF.C.9 Questions

(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

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Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 7?
  1. Substitution Property of Equality
  2. Addition Property of Equality
  3. Identity Property
  4. Pythagorean Theorem
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]cos(105°) ?[/math]
  1. [math](sqrt(2)-sqrt(6))/4[/math]
  2. [math]-(sqrt(2)+sqrt(6))/4[/math]
  3. [math]-1/2 + sqrt(6)/4[/math]
  4. [math](sqrt(6)-sqrt(2))/4[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]sin(345°) ?[/math]
  1. [math]1/2(sqrt(2)-1)[/math]
  2. [math]-1/4 (sqrt(2)+sqrt(6))[/math]
  3. [math]1/4(sqrt(6) - sqrt(2))[/math]
  4. [math]1/4(sqrt(2) - sqrt(6))[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 10?
  1. Trigonometric Identity
  2. Length of a line segment
  3. Pythagorean Identity
  4. Law of Sines
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]tan(75°) ?[/math]
  1. [math]-2+sqrt(3)[/math]
  2. [math]2+sqrt(3)[/math]
  3. [math]1[/math]
  4. [math]2-sqrt(3)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]tan(165°) ?[/math]
  1. [math]2-sqrt(3)[/math]
  2. [math]-2-sqrt(3)[/math]
  3. [math]2+sqrt(3)[/math]
  4. [math]-2+sqrt(3)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing statement in step 13?
  1. [math]AB^2 = cos^2(alpha)sin^2(alpha) + cos^2(theta) sin^2(theta) - 2cos(alpha)sin(alpha)cos(theta)sin(theta)[/math]
  2. [math]AB^2 = cos^2(alpha) - 2cos(alpha)sin(alpha) + sin^2(alpha) + cos^2(theta) - 2cos(theta)sin(theta) + sin^2(theta)[/math]
  3. [math]AB^2 = cos^2(alpha) - 2cos(alpha)cos(theta) + cos^2(theta) + sin^2(alpha) - 2sin(alpha)sin(theta) + sin^2(theta)[/math]
  4. [math]AB^2 = cos^2(alpha) + cos^2(theta) + sin^2(alpha) + sin^2(theta)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the value of [math]cos(165°) ?[/math]
  1. [math]1/4(sqrt(2)-sqrt(6))[/math]
  2. [math]-1/4(sqrt(2)+sqrt(6))[/math]
  3. [math]1/4(-sqrt(2)+sqrt(6))[/math]
  4. [math]1/2(-sqrt(2)+sqrt(3))[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]sin(105°) ?[/math]
  1. [math]1/2(sqrt(3)+sqrt(2))[/math]
  2. [math]1/4(sqrt(2)-sqrt(6))[/math]
  3. [math]1/4(sqrt(6)+sqrt(2))[/math]
  4. [math]1/4(sqrt(6)-sqrt(2))[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 15?
  1. Addition Property of Equality
  2. Pythagorean Identity
  3. Substitution Property of Equality
  4. Given
Grade 11 Trigonometry CCSS: HSF-TF.C.9
What is the exact value of [math]sin(195°) ?[/math]
  1. [math]-1/2(sqrt(2)+sqrt(3))[/math]
  2. [math]-1/4(sqrt(6) + sqrt(2))[/math]
  3. [math]1/4(sqrt(2) - sqrt(6))[/math]
  4. [math]1/4(sqrt(6) - sqrt(2))[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 18?
  1. Reciprocal Identity
  2. Radii of the same circle are equal
  3. Transitive Property of Equality
  4. Pythagorean Theorem
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing expression in step 5?
  1. [math]( ( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))[/math]
    [math] \ \ [/math]
  2. [math]( ( \ cos(alpha)cos(beta) \ )( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/(( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))[/math]
    [math] \ \ [/math]
  3. [math]( ( \ cos(alpha)cos(beta) \ )( \ sin(alpha)cos(beta) + sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ cos(alpha)cos(beta) - sin(alpha)sin(beta) \ ))[/math]
    [math] \ \ [/math]
  4. [math]( ( \ sin(alpha)cos(beta) \ )( \ sin(beta)cos(alpha) \ ))/( ( \ cos(alpha)cos(beta) \ ) ( \ sin(alpha)sin(beta) \ ))[/math]
    [math] \ \ [/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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Which of the following is equal to [math]cos(-theta) ?[/math]
  1. [math]cos(theta)[/math]
  2. [math]-cos(theta)[/math]
  3. [math]-cos(-theta)[/math]
  4. [math]cos(theta-1)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 1?
  1. [math]"Definition of tangent"[/math]
  2. [math]"Pythagorean Identity"[/math]
  3. [math]"Law of S""ines"[/math]
  4. [math]alpha/alpha = 1, \ beta/beta = 1[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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Which of the following is equal to [math]sin(-theta) ?[/math]
  1. [math]sin(theta)[/math]
  2. [math]-sin(theta)[/math]
  3. [math]-sin(-theta)[/math]
  4. [math]sin(theta-1)[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing expression in step 2?
  1. [math](((sin(alpha)cos(beta))/(cos(alpha)sin(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))[/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math]
  2. [math](((sin(alpha)sin(beta))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))[/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math]
  3. [math](((sin(alpha)cos(alpha) \ + \ sin(beta)cos(beta))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))[/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math] [math] \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [/math]
  4. [math](((sin(alpha)cos(beta) \ + \ sin(beta)cos(alpha))/(cos(alpha)cos(beta))))/((1-sin(alpha)/cos(alpha) sin(beta)/cos(beta)))[/math]
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