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Common Core Standard HSF-TF.C.8 Questions

Prove the Pythagorean identity sin2(θ) + cos2(θ) = 1 and use it to find sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.

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Grade 11 Trigonometry CCSS: HSF-TF.C.8
Which of the following is an alternate form of the Pythagorean Identity? Choose all correct answers.
  1. tan2(θ)+sin2(θ)=1
  2. tan2(θ)+1=sec2(θ)
  3. 1+sec2(θ)=cot2(θ)
  4. 1+cot2(θ)=csc2(θ)
Grade 11 Trigonometry CCSS: HSF-TF.C.8
If tan(θ)=√1111 and π<θ<3π2, what is the value of sec(θ)?
  1. -2√3311
  2. √11011
  3. 2√3311
  4. -√11011
Grade 11 Trigonometry CCSS: HSF-TF.C.8
Given that cos(θ)=37 and 0<θ<π2, what is the value of sin(θ)?
  1. 2√107
  2. 4049
  3. √587
  4. 5849
Grade 11 Trigonometry CCSS: HSF-TF.C.8
If csc(θ)=-7√33 and 3π2<θ<2π, what is the value of cot(θ)?
  1. -√1383
  2. √1383
  3. 2√393
  4. -2√393
Grade 11 Trigonometry CCSS: HSF-TF.C.8
If tan(θ)=-49 and π2<θ<π, what is the value of sin(θ)?
  1. 4√9797
  2. √974
  3. 9√9797
  4. 9√6565
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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What is the missing reason in step 2?
  1. Given
  2. Pythagorean Theorem
  3. Law of Sines
  4. Summation Property of Addition
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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What is the missing statement in step 6?
  1. sin(ϕ)=ac
  2. sin(θ)=ab
  3. sin(θ)=bc
  4. sin(θ)=ac
Grade 11 Trigonometry CCSS: HSF-TF.C.8
If sin(θ)=√54 and π2<θ<π, what is the value of sec(θ)?
  1. -√114
  2. -4√2121
  3. √114
  4. -4√1111
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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What is the missing statement in step 7?
  1. cos(θ)=bc
  2. cos(θ)=ac
  3. cos(θ)=ab
  4. cos(ϕ)=bc
Grade 11 Trigonometry CCSS: HSF-TF.C.8
What is the value of cos(θ) if cot(θ)=19 and π<θ<3π2?
  1. -√8282
  2. -√1010
  3. -√520
  4. -√24
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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What is the missing reason in step 8?
  1. Substitution Property of Equality
  2. Given
  3. Pythagorean Theorem
  4. Trigonometric Identity
Grade 11 Trigonometry CCSS: HSF-TF.C.8
What is the value of tan(θ) if sin(θ)=-38 and 3π2<θ<2π?
  1. -√553
  2. -3√5555
  3. -√733
  4. -3√7373
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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Which of the following gives the length of ¯TP?
  1. sin(θ)
  2. cos(θ)
  3. sin(α)
  4. cos(α)
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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Which of the following gives the length of ¯PO?
  1. cos(α)
  2. sin(θ)
  3. cos(θ)
  4. sin(α)
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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Which of the following is true?
  1. cos(θ)=cos(α) for 0<θ<π2, but otherwise these two quantities are never equal.
  2. cos(θ)=±cos(α) for all values of θ.
  3. cos(θ)=-cos(α) for all values of θ.
  4. cos(θ) and cos(α) are never equal.
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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Which of the following is true?
  1. sin(θ)=±sin(α) for 0≤θ≤π. Otherwise, these quantities are not equal.
  2. sin(θ)=±sin(α) for 0≤θ≤π2. Otherwise, these quantities are not equal.
  3. sin(θ) and sin(α) are never equal.
  4. sin(θ)=±sin(α) for all values of θ.
Grade 11 Trigonometry CCSS: HSF-TF.C.8

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For 0<θ<2π,θ≠π2,π,3π2, what type of triangle is ΔTPO?
  1. Right triangle.
  2. Acute triangle.
  3. It depends on the quadrant.
  4. Obtuse triangle.

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