alleryStart learning →The reciprocal and quotient identities are derived from what?
AThe properties of a right triangle and its sides
BThe addition formulas for sine and for cosine
CThe definitions of the basic trigonometric functions
DThe graphs of the six trigonometric functions
Answer & Solution
Correct answer: C. The definitions of the basic trigonometric functions
1. The reciprocal identities state relations such as csc x = 1 / sin x and sec x = 1 / cos x.
2. The quotient identities state tan x = sin x / cos x and cot x = cos x / sin x.
3. Both families fall straight out of the definitions of the basic trigonometric functions and need no further construction.
4. The Pythagorean identities are the ones that lean on right triangle properties, so that option confuses the two families.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.1 Solving Trigonometric Equations with Identities_
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