alleryStart learning →Compared with y = sin t, the graph of y = sin(2t) is which transformation?
AA horizontal compression by a factor of 2
BA horizontal stretch by a factor of 2
CA vertical compression by a factor of 2
DA vertical stretch by a factor of 2
Answer & Solution
Correct answer: A. A horizontal compression by a factor of 2
1. Doubling the input makes the curve complete its cycle in half the horizontal distance.
2. So y = sin(2t) is a horizontal compression of y = sin t by a factor of 2.
3. Two full periods now fit inside an interval of length 2 pi instead of one.
4. That doubling is why sin(2t) = 0 has twice as many solutions as sin t = 0 on the same interval.
5. The amplitude is untouched, so no vertical stretch or compression occurs.
_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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