The period of y = 2Sin(x - \pi/3) is ________.

Question

Accepted Answer

{"content":[{"type":"paragraph","content":[{"text":"Step 1 (State Periodicity Formula):","type":"text","marks":[{"type":"bold"}]},{"text":" The standard sine function ","type":"text"},{"attrs":{"latex":"y = A \sin(kx + \theta)"},"type":"math_inline"},{"text":" has a period ","type":"text"},{"attrs":{"latex":"T"},"type":"math_inline"},{"type":"text","text":" given by the formula:"}]},{"attrs":{"latex":"T = \frac{2\pi}{|k|}"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 2 (Identify Parameters):","type":"text"},{"text":" In our function ","type":"text"},{"type":"math_inline","attrs":{"latex":"y = 2 \sin(x - \pi/3)"}},{"text":":","type":"text"}],"type":"paragraph"},{"content":[{"content":[{"type":"paragraph","content":[{"text":"The coefficient of ","type":"text"},{"attrs":{"latex":"x"},"type":"math_inline"},{"text":" is ","type":"text"},{"type":"math_inline","attrs":{"latex":"k = 1"}}]}],"type":"list_item"},{"type":"list_item","content":[{"content":[{"text":"The shift is ","type":"text"},{"attrs":{"latex":"\theta = -\pi/3"},"type":"math_inline"}],"type":"paragraph"}]}],"type":"bullet_list"},{"content":[{"text":"Substituting ","type":"text"},{"attrs":{"latex":"k = 1"},"type":"math_inline"},{"text":" into the formula:","type":"text"}],"type":"paragraph"},{"attrs":{"latex":"T = \frac{2\pi}{1} = 2\pi"},"type":"math_block"},{"content":[{"marks":[{"type":"bold"}],"text":"Step 3 (Conclusion):","type":"text"},{"type":"text","text":" The period of the function is exactly "},{"type":"text","marks":[{"type":"code"}],"text":"2pi"},{"text":".","type":"text"}],"type":"paragraph"}],"type":"doc"}

Guide / Hint

Solution