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Why does a trigonometric equation have infinitely many solutions unless the domain is restricted?
AThe functions are always positive
BThe functions repeat periodically
CThe functions have no maximum
DThe functions are not continuous
Answer & Solution
Correct answer: B. The functions repeat periodically
1. Sine, cosine and tangent all repeat their values after a fixed interval of angle.
2. So once one angle satisfies an equation, adding whole periods to it gives more angles that also satisfy it.
3. Subtracting whole periods works in the same way and gives negative angles.
4. That is why a general solution is written with a whole number of periods added on.
_Source: Siyavula Mathematics Grade 12 (Everything Maths, CC BY 4.0), Chapter 4: Trigonometry_
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