alleryStart learning →Solving sin(n t) = c across one turn requires going around the unit circle how many times?
AOnce, regardless of the value of n
BTwice, regardless of the value of n
Cn times, once for each compression
DHalf of n times, rounded upward
Answer & Solution
Correct answer: C. n times, once for each compression
1. Writing n t as a single angle means that angle sweeps n full turns while t sweeps one.
2. Every extra turn of the inner angle produces another pair of candidate solutions for t.
3. So the unit circle must be traversed n times before the list is complete.
4. Each candidate is then divided by n and kept only if it still lies in the required interval for t.
5. Going round once would find only the first pair and quietly discard the rest.
_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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