find sin s.\ncos s = \\frac{1}{2} and s is in quadrant i.\nsin s = \\square\n(simplify your answer…

Explanation:

Step1: Use the Pythagorean identity

The Pythagorean identity is $\sin^{2}s+\cos^{2}s = 1$.

Step2: Substitute the given value of $\cos s$

Given $\cos s=\frac{1}{2}$, substitute it into the identity: $\sin^{2}s+\left(\frac{1}{2}\right)^{2}=1$. So, $\sin^{2}s+\frac{1}{4}=1$.

Step3: Solve for $\sin^{2}s$

Subtract $\frac{1}{4}$ from both sides: $\sin^{2}s=1 - \frac{1}{4}=\frac{4 - 1}{4}=\frac{3}{4}$.

Step4: Take the square root

Since (s) is in quadrant I and (\sin s>0) in quadrant I, (\sin s=\sqrt{\frac{3}{4}}). Simplify (\sqrt{\frac{3}{4}}=\frac{\sqrt{3}}{2}).

Answer:

(\frac{\sqrt{3}}{2})