Special Relationships Between Sine and Cosine, #2 (Grades 11-12)

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Special Relationships Between Sine and Cosine, #2

1. 
Find the value of [math]theta[/math], [math]0° < theta < 90°[/math], if [math]sin(35°) = cos(theta)[/math].
  1. 10°
  2. 35°
  3. 45°
  4. 55°
2. 
Find the value of [math]theta, \ 0 < theta < 90°[/math], if [math]cos(15) = sin(theta)[/math].
  1. 15°
  2. 45°
  3. 30°
  4. 75°
3. 
Find the value of [math]theta, \ 0° < theta < 90°[/math], if [math]cos(theta) = sin(45°)[/math].
  1. 45°
  2. 55°
  3. 90°
  4. No such angle exists.
4. 
Find the value of [math]theta, \ 0° < theta < 90°[/math], if [math]sin(theta) = cos(83°)[/math].
  1. 38°
  2. 45°
  3. 83°
5. 
Find the value of [math]x[/math] if [math]sin((2x+3)°) = cos((3x-13)°)[/math] and both angles are between 0° and 90°.
  1. [math]16[/math]
  2. [math]74/5[/math]
  3. [math]20[/math]
  4. [math]106/5[/math]
6. 
Find the value of [math]x[/math] if [math]sin((3x)°) = cos((14x+5)°)[/math] and both angles are between 0° and 90°.
  1. There is no value of [math]x[/math] such that the equation is true and both angles are between 0° and 90°.
  2. [math]5[/math]
  3. [math]85/11[/math]
  4. [math]95/17[/math]
7. 
Find the value of [math]x[/math] if [math]sin((2x+5)°) = cos((4x-35)°)[/math] and both angles are between 0° and 90°.
  1. [math]25/3[/math]
  2. [math]15[/math]
  3. [math]20[/math]
  4. [math]65/3[/math]
8. 
Find the value of [math]x[/math] if [math]sin((4x-7)°) = cos((3x+24)°)[/math] and both angles are between 0° and 90°.
  1. [math]59/7[/math]
  2. [math]73/7[/math]
  3. [math]121/7[/math]
  4. [math]31[/math]
9. 
Find the value of [math]x[/math] if [math]sin((6x+3)°) = cos((4x^2-1)°)[/math] and both angles are between 0° and 90°.
  1. [math]1/2[/math]
  2. [math]2[/math]
  3. [math]4[/math]
  4. [math]29/2[/math]
10. 
Find the value of [math]x[/math] if [math]sin((2x^2 + 10x + 30)°) = cos((-x^2 - 14x + 62)°)[/math] and both angles are between 0° and 90°. Choose all correct answers. Round the answer(s) to two decimal places.
  1. 0.59
  2. 1.16
  3. 3.41
  4. 13.2

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