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Use the Pythagorean identities to find all trig functions from one known value.
From the unit circle: Any point on the unit circle is (cos θ, sin θ), and since x² + y² = 1:
Dividing by cos²θ:
Dividing by sin²θ:
The Pythagorean identity gives you the magnitude but not the sign. The quadrant determines whether each function is positive or negative.
Use sin² + cos² = 1 when you know sin or cos. Use the tan-sec identity when dealing with tangent problems. Use cot-csc when dealing with cotangent problems.