Pythagorean identity (sin² + cos² = 1)
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Consider a point \(P\) on the unit circle (the circle of radius \(1\) centered at the origin). The point's coordinates are \((\cos\theta, \sin\theta)\) where \(\theta\) is the angle from the positive \(x\)-axis.
(i) What is the equation of the unit circle?
(ii) Substitute \(x = \cos\theta\) and \(y = \sin\theta\) into the unit-circle equation.
(iii) State the resulting identity. This is the \(\textbf{Pythagorean identity}\).
(ii) \(\cos^2\theta + \sin^2\theta = 1\).
(iii) \(\sin^2\theta + \cos^2\theta = 1\) — the Pythagorean identity
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