alleryStart learning →The domain of the tangent function excludes which set of angles?
AThe even integer multiples of pi / 2
BThe odd integer multiples of pi / 2
CThe odd integer multiples of pi / 4
DThe whole integer multiples of 2 pi
Answer & Solution
Correct answer: B. The odd integer multiples of pi / 2
1. Tangent is sine divided by cosine, so it fails wherever cosine is zero.
2. Cosine vanishes at pi/2, at 3 pi/2, at 5 pi/2 and so on.
3. Those are exactly the odd integer multiples of pi / 2.
4. The even multiples of pi / 2 are the multiples of pi, where cosine equals plus or minus 1 and tangent is perfectly well defined.
_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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