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Common Core Standard HSG-SRT.C.7 Questions

Explain and use the relationship between the sine and cosine of complementary angles.

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Grade 11 Trigonometry CCSS: HSG-SRT.C.7
ΔFGH is a right triangle and ∠G is a right angle. If cos(F)=cos(H), what are the measures of the acute angles in this triangle?
  1. They are both equal and can be anything less than 45° (and greater than 0°).
  2. They are both 45°.
  3. The angles measures are 30° and 60°.
  4. No such triangle exists.
Grade 11 Trigonometry CCSS: HSG-SRT.C.7
ΔXYZ is a right triangle and ∠Y is a right angle. If cos(2X)=sin(X), what are the measures of the acute angles in this triangle?
  1. The angles measures are 30° and 60°.
  2. The angle measures are 22.5° and 45°.
  3. Only the measure of ∠X can be determined, and it is 30°.
  4. There is no such triangle.
Grade 11 Trigonometry CCSS: HSG-SRT.C.7
Referring to ΔABC, what is the value of sin(B)+cos(C)2, fully simplified?
Right Triangle ABC v1
  1. AC2BC
  2. AC+AB2BC
  3. ABBC
  4. ACBC
Grade 11 Trigonometry CCSS: HSG-SRT.C.7, HSG-SRT.C.8
Referring to ΔABC, what is the value of sin2(B)+sin2(A), fully simplified?
Right Triangle ABC v3
  1. 2AC2(AB)2
  2. 2BC2(AB)2
  3. 1
  4. 2AB
Grade 11 Trigonometry CCSS: HSG-SRT.C.7
Right triangles are NEVER obtuse.
  1. True
  2. False
Grade 11 Trigonometry CCSS: HSG-SRT.C.7
In ΔABC, which of the following is/are equal to sin(A)? There may be more than one correct answer.
Right Triangle ABC v3
  1. cos(B)
  2. cos(90°-A)
  3. sin(90°-B)
  4. sin(B)
Grade 11 Trigonometry CCSS: HSG-SRT.C.7
In ΔABC, which of the following is/are equal to ABBC? There may be more than one correct answer.
Right Triangle ABC v1
  1. sin(C)
  2. cos(B)
  3. sin(90°-B)
  4. cos(90°-C)
Grade 11 Trigonometry CCSS: HSG-SRT.C.7
Find the value of x if sin((3x)°)=cos((14x+5)°) and both angles are between 0° and 90°.
  1. There is no value of x such that the equation is true and both angles are between 0° and 90°.
  2. 5
  3. 8511
  4. 9517
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