alleryStart learning →What distinguishes a trigonometric identity from a trigonometric equation?
AAn identity holds only on a bounded interval
BAn identity holds for every value in the domain
CAn identity holds only at the special angles
DAn identity holds for exactly two values
Answer & Solution
Correct answer: B. An identity holds for every value in the domain
1. An identity is a statement that is true for all values in the domain of the variable.
2. A trigonometric equation, by contrast, is satisfied only by particular values, if any exist at all.
3. So sin^2 x + cos^2 x = 1 is an identity, while sin x = 1/2 is an equation with selected solutions.
4. Holding only at the special angles would make a statement an equation, not an identity.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 9 "Trigonometric Identities and Equations", section 9.5 Solving Trigonometric Equations_
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