alleryStart learning →Among the six trigonometric functions, which two are even?
ASine and cosecant
BTangent and cotangent
CSine and cosine
DCosine and secant
Answer & Solution
Correct answer: D. Cosine and secant
1. An even function satisfies f(-x) = f(x), and cos(-x) = cos x, so cosine is even.
2. Secant is the reciprocal of cosine, so sec(-x) = 1 / cos(-x) = 1 / cos x = sec x, making secant even too.
3. Sine, cosecant, tangent and cotangent all reverse sign under a negative angle, so those four are odd.
4. Exactly two functions are even, and they are cosine and secant.
_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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