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.
- True
- False
2.
Right triangles are NEVER obtuse.
- True
- 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.

- [math]sin(B)[/math]
- [math]sin(C)[/math]
- [math]cos(B)[/math]
- [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.

- [math](AC)/(BC)[/math]
- [math]sin(B)[/math]
- [math]cos(B)[/math]
- [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.

- [math]cos(B)[/math]
- [math]cos(90° - A)[/math]
- [math]sin(90° - B)[/math]
- [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.

- [math]sin(C)[/math]
- [math]cos(B)[/math]
- [math]sin(90°-B)[/math]
- [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?
- They are both equal and can be anything less than 45° (and greater than 0°).
- They are both 45°.
- The angles measures are 30° and 60°.
- 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?
- The angles measures are 30° and 60°.
- The angle measures are 22.5° and 45°.
- Only the measure of [math]ang X[/math] can be determined, and it is 30°.
- 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?

- [math](AC)/(2BC)[/math]
- [math](AC+AB)/(2BC)[/math]
- [math](AB)/(BC)[/math]
- [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?

- [math](2AC^2)/(AB)^2 [/math]
- [math](2BC^2)/(AB)^2 [/math]
- [math]1[/math]
- [math]2/(AB)[/math]
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