Prove and use sin^2(theta)+cos^2(theta)=1 to find trig values with quadrant information.
Determine whether given sine and cosine values are possible for the same angle
Problem
Determine whether trig values \(\sin~\theta=0.6,~\cos~\theta=0.8\) are possible.
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What this problem is really about
A proposed sine-cosine pair must pass both a magnitude test and any sign constraints. We’ll confirm each value is in range, add their squares rather than the values themselves, and interpret the signs as coordinates of a possible unit-circle point.
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