Quotient identities rewrite tangent and cotangent using sine and cosine. This is useful when expressions need to be simplified into the two fundamental functions.
⚠Tangent is undefined if cosine is zero, and cotangent is undefined if sine is zero.
How Quotient Identities Work
Tangent compares sine to cosine, while cotangent compares cosine to sine. The two functions are reciprocals when both are defined.
Tangent
tan θ = sin θ / cos θ.
Cotangent
cot θ = cos θ / sin θ.
Undefined Cases
Watch for zero denominators.
Simplification
Useful for rewriting expressions.
💡 Example: If sin=0.5 and cos=0.866025, then tan=0.57735 and cot=1.732051.
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