Trigonometry · Intermediate · 9 min
A circle full of identities
The most familiar trig identity is just the Pythagorean theorem on a circle of radius one.
WHAT HAPPENS IF…Try angles in all four quadrants. Does the sum ever change?
Preparing your experiment…
The coordinates of a unit-circle point satisfy x² + y² = 1. Substituting x = cos θ and y = sin θ proves the identity, including quadrants where a coordinate is negative.
A detail that matters
sin² θ means (sin θ)², not sin(θ²).
Keep the connection going
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