Prove and use sin^2(theta)+cos^2(theta)=1 to find trig values with quadrant information.
Use the Pythagorean identity to find sine when cosine and the quadrant are known
Problem
Use the \(\text{Pythagorean}~\text{identity}\) to find \(\text{sine}\) when \(\cos(\theta)=3/5\) and \(\theta\) is in \(\text{Quadrant}~I\).
Big Picture
What this problem is really about
The Pythagorean identity determines the missing trig magnitude, while the quadrant determines its sign. We’ll substitute the known cosine, isolate sine squared, take both algebraic square roots, and then use the terminal point’s vertical coordinate to resolve the sign.
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