Questions: Find one solution for the equation. Assume that all angles involved are acute angles. sin(2θ-50°)=cos(3θ+15°)

Solution Steps

Given the equation: \[ \sin(2\theta - 50^\circ) = \cos(3\theta + 15^\circ) \]

We use the property that \(\sin(x) = \cos(90^\circ - x)\). Therefore, we can set up the equation: \[ 2\theta - 50^\circ + 3\theta + 15^\circ = 90^\circ \]

Combine like terms: \[ 2\theta + 3\theta - 50^\circ + 15^\circ = 90^\circ \] \[ 5\theta - 35^\circ = 90^\circ \]

Add \(35^\circ\) to both sides of the equation: \[ 5\theta = 90^\circ + 35^\circ \] \[ 5\theta = 125^\circ \]

Divide both sides by 5: \[ \theta = \frac{125^\circ}{5} \] \[ \theta = 25^\circ \]

Final Answer