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

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What is the missing explanation in step 3?
  1. [math]"The sine and cosine functions are never greater than 1"[/math]
  2. [math]cos^2(theta)+ sin^2(theta)=1[/math]
  3. [math]cos(0)=1, \ sin(90°)=1[/math]
  4. [math]"The number 1 can be rewritten as a given quantity divided by itself"[/math]
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 4?
  1. Distributive Property of Multiplication
  2. Commutative Property of Multiplication
  3. SSA formula for area of a triangle
  4. Law of Sines
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 6?
  1. Pythagorean Identity
  2. Cancel like factors
  3. Substitution Property of Equality
  4. Division Property of Identity
Grade 12 Trigonometry CCSS: HSF-TF.C.9

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What are some of the implicit restrictions in the above proof? Choose all correct answers.
  1. [math]0 < theta+alpha < pi[/math], where [math]theta,alpha[/math] must both be positive real numbers.
  2. [math]0 < theta+alpha < pi/2[/math], where [math]theta, alpha[/math] must both be positive real numbers.
  3. [math]Delta ABC[/math] cannot be a right triangle.
  4. [math]ang BAC[/math] and [math] angBCA[/math] must both be acute angles.
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing reason in step 7?
  1. Given
  2. Right triangles have 2 sets of perpendicular sides
  3. Triangle Property
  4. SSS Property of Similarity
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 7?
  1. Substitute in the sine addition formula
  2. Apply the Law of Sines
  3. Cancel like terms
  4. Factor out like terms
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing statement in step 9?
  1. [math]ang ABC[/math] is a right angle
  2. Point [math]D[/math] is the midpoint of [math]bar{AC}[/math]
  3. [math]ang ABC[/math] is acute
  4. [math]ang ADB, \ ang BDC[/math] are right angles
Grade 11 Trigonometry CCSS: HSF-TF.C.9

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What is the missing explanation in step 8?
  1. Substitute in the cosine addition formula
  2. Apply the Law of Cosines
  3. Cancel like terms
  4. Factor out like terms
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