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Find the acute angle solution to the following equation involving cofunctions. θ is in degrees. cos(2θ+15)=sin(5θ+12)
A
1°
B
4°
C
6°
D
9°
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1
Recognize that the equation involves cofunctions: \( \cos(2\theta + 15) = \sin(5\theta + 12) \). Cofunctions are related by the identity \( \cos(\theta) = \sin(90^\circ - \theta) \).
Apply the cofunction identity to rewrite the equation: \( \cos(2\theta + 15) = \sin(90^\circ - (2\theta + 15)) \).
Set the expressions inside the sine function equal to each other: \( 90^\circ - (2\theta + 15) = 5\theta + 12 \).
Simplify the equation: \( 90^\circ - 2\theta - 15 = 5\theta + 12 \). Combine like terms to form a linear equation in terms of \( \theta \).
Solve the linear equation for \( \theta \) to find the acute angle solution. Ensure \( \theta \) is within the range of acute angles, which is between \( 0^\circ \) and \( 90^\circ \).