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Trigonometric Graphs: Sine and Cosine - A guide to understanding amplitude, period, phase shift, and vertical shift with example equations and graphs.

A detailed educational infographic on trigonometric graphs of sine and cosine functions, showing equations, parameters, and two graphs illustrating y = sin x and y = -3 sin 2(x - π/4) + 1.

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Show Answer Key & Explanations Step-by-step solution for: Graphing Sin and Cos | Trigonometric functions, Writing equations ...

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- A = 3 (amplitude, the absolute value of the coefficient of the sine function)
- B = 2 (coefficient affecting the period)
- Period = π (calculated as 2π / B = 2π / 2)
- Phase shift (h) = π/4 (the horizontal shift, found from the term (x - π/4))
- Vertical shift (k) = 1 (the constant added at the end, which is the center line)
- Graphing window: x ranges from -3π/4 to 5π/4 (determined by solving -π ≤ x - π/4 ≤ π)

Parent Tip: Review the logic above to help your child master the concept of sine and cosine graphs worksheet.

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