Sine and Cosine of Complementary Angles (Grades 11-12)

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Sine and Cosine of Complementary Angles

1. 
In a right triangle, the two non-right angles are ALWAYS complementary.
  1. True
  2. False
2. 
Right triangles are NEVER obtuse.
  1. True
  2. False
3. 
In [math]Delta ABC[/math], which of the following is/are equal to [math](AB)/(BC) ?[/math] There may be more than one correct answer.
Right Triangle ABC v2
  1. [math]sin(B)[/math]
  2. [math]sin(C)[/math]
  3. [math]cos(B)[/math]
  4. [math]cos(C)[/math]
4. 
In [math]Delta ABC[/math], which of the following is/are equal to [math]cos(C) ?[/math] There may be more than one correct answer.
Right Triangle ABC v2
  1. [math](AC)/(BC)[/math]
  2. [math]sin(B)[/math]
  3. [math]cos(B)[/math]
  4. [math](AB)/(BC)[/math]
5. 
In [math]Delta ABC[/math], which of the following is/are equal to [math]sin(A) ?[/math] There may be more than one correct answer.
Right Triangle ABC v3
  1. [math]cos(B)[/math]
  2. [math]cos(90° - A)[/math]
  3. [math]sin(90° - B)[/math]
  4. [math]sin(B)[/math]
6. 
In [math]Delta ABC[/math], which of the following is/are equal to [math](AB)/(BC) ?[/math] There may be more than one correct answer.
Right Triangle ABC v1
  1. [math]sin(C)[/math]
  2. [math]cos(B)[/math]
  3. [math]sin(90°-B)[/math]
  4. [math]cos(90°-C)[/math]
7. 
[math]Delta FGH[/math] is a right triangle and [math]ang G[/math] is a right angle. If [math]cos(F) = cos(H)[/math], 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.
8. 
[math]Delta XYZ[/math] is a right triangle and [math]ang Y[/math] is a right angle. If [math]cos(2X) = sin(X)[/math], 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 [math]ang X[/math] can be determined, and it is 30°.
  4. There is no such triangle.
9. 
Referring to [math]Delta ABC[/math], what is the value of [math](sin(B)+cos(C))/2[/math], fully simplified?
Right Triangle ABC v1
  1. [math](AC)/(2BC)[/math]
  2. [math](AC+AB)/(2BC)[/math]
  3. [math](AB)/(BC)[/math]
  4. [math](AC)/(BC)[/math]
10. 
Referring to [math]Delta ABC[/math], what is the value of [math]sin^2(B) + sin^2(A)[/math], fully simplified?
Right Triangle ABC v3
  1. [math](2AC^2)/(AB)^2 [/math]
  2. [math](2BC^2)/(AB)^2 [/math]
  3. [math]1[/math]
  4. [math]2/(AB)[/math]

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