Prove and use sin^2(theta)+cos^2(theta)=1 to find trig values with quadrant information.
Use the Pythagorean identity to find cosine when sine and the quadrant are known
Problem
Use the \(\text{Pythagorean}~\text{identity}\) to find \(\text{cosine}\) when \(\sin(\theta)=4/5\) and \(\theta\) is in Quadrant \(I\).
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What this problem is really about
Finding a missing cosine has two stages: calculate its magnitude from the identity, then assign its sign from location. We’ll substitute the known sine, isolate cosine squared, take the square root, and connect cosine to the terminal point’s horizontal coordinate.
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