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].
- 10°
- 35°
- 45°
- 55°
2.
Find the value of [math]theta, \ 0 < theta < 90°[/math], if [math]cos(15) = sin(theta)[/math].
- 15°
- 45°
- 30°
- 75°
3.
Find the value of [math]theta, \ 0° < theta < 90°[/math], if [math]cos(theta) = sin(45°)[/math].
- 45°
- 55°
- 90°
- No such angle exists.
4.
Find the value of [math]theta, \ 0° < theta < 90°[/math], if [math]sin(theta) = cos(83°)[/math].
- 7°
- 38°
- 45°
- 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°.
- [math]16[/math]
- [math]74/5[/math]
- [math]20[/math]
- [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°.
- There is no value of [math]x[/math] such that the equation is true and both angles are between 0° and 90°.
- [math]5[/math]
- [math]85/11[/math]
- [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°.
- [math]25/3[/math]
- [math]15[/math]
- [math]20[/math]
- [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°.
- [math]59/7[/math]
- [math]73/7[/math]
- [math]121/7[/math]
- [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°.
- [math]1/2[/math]
- [math]2[/math]
- [math]4[/math]
- [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.
- 0.59
- 1.16
- 3.41
- 13.2
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