Answer
$$\sin\theta=\frac{\sqrt 7}{4}$$
Work Step by Step
$$\cos\theta=\frac{3}{4}$$
To find $\sin\theta$, we would use the Pythagorean Identity $$\sin^2\theta+\cos^2\theta=1$$ $$\sin^2\theta=1-\cos^2\theta$$
Apply $\cos\theta=\frac{3}{4}$ here, we have $$\sin^2\theta=1-(\frac{3}{4})^2=1-\frac{9}{16}=\frac{7}{16}$$ $$\sin\theta=\pm\frac{\sqrt 7}{4}$$
We know that $\theta$ is in quadrant I, which means $\sin\theta$ is positive.
Therefore, $$\sin\theta=\frac{\sqrt 7}{4}$$
