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This printable supports Common Core Mathematics Standard HSG-SRT.C.7

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# 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 $theta$, $0° < theta < 90°$, if $sin(35°) = cos(theta)$.
1. 10°
2. 35°
3. 45°
4. 55°
2.
Find the value of $theta, \ 0 < theta < 90°$, if $cos(15) = sin(theta)$.
1. 15°
2. 45°
3. 30°
4. 75°
3.
Find the value of $theta, \ 0° < theta < 90°$, if $cos(theta) = sin(45°)$.
1. 45°
2. 55°
3. 90°
4. No such angle exists.
4.
Find the value of $theta, \ 0° < theta < 90°$, if $sin(theta) = cos(83°)$.
1. 38°
2. 45°
3. 83°
5.
Find the value of $x$ if $sin((2x+3)°) = cos((3x-13)°)$ and both angles are between 0° and 90°.
1. $16$
2. $74/5$
3. $20$
4. $106/5$
6.
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. $85/11$
4. $95/17$
7.
Find the value of $x$ if $sin((2x+5)°) = cos((4x-35)°)$ and both angles are between 0° and 90°.
1. $25/3$
2. $15$
3. $20$
4. $65/3$
8.
Find the value of $x$ if $sin((4x-7)°) = cos((3x+24)°)$ and both angles are between 0° and 90°.
1. $59/7$
2. $73/7$
3. $121/7$
4. $31$
9.
Find the value of $x$ if $sin((6x+3)°) = cos((4x^2-1)°)$ and both angles are between 0° and 90°.
1. $1/2$
2. $2$
3. $4$
4. $29/2$
10.
Find the value of $x$ if $sin((2x^2 + 10x + 30)°) = cos((-x^2 - 14x + 62)°)$ 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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