Prove and use sin^2(theta)+cos^2(theta)=1 to find trig values with quadrant information.
Find an exact trigonometric value using the identity when one trig value and the quadrant are known
Problem
Given \(\cos~\theta=1/3\) and \(\text{Quadrant}~I\), use the Pythagorean identity to find \(\sin~\theta\).
Big Picture
What this problem is really about
Exact trig work keeps the square-root magnitude separate from the quadrant sign. We’ll use the identity to find the missing square, simplify the radical without decimal approximation, and then use the terminal point’s coordinate signs to determine the correct root.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
