Solve each equation for exact solutions.
arcsin x = arctan 3/4

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Recognize that the equation is \( \arcsin x = \arctan \frac{3}{4} \), which means the angle whose sine is \( x \) is equal to the angle whose tangent is \( \frac{3}{4} \).

Let \( \theta = \arctan \frac{3}{4} \). This means \( \tan \theta = \frac{3}{4} \). We want to find \( x = \sin \theta \).

Use the right triangle definition of tangent: if \( \tan \theta = \frac{3}{4} \), then the opposite side is 3 and the adjacent side is 4. Calculate the hypotenuse using the Pythagorean theorem: \( \text{hypotenuse} = \sqrt{3^2 + 4^2} \).

Find \( \sin \theta \) using the triangle sides: \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{\sqrt{3^2 + 4^2}} \).

Since \( \arcsin x = \theta \), the exact solution for \( x \) is \( \sin \theta \) as found above.

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