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MathTrigonometry

Graph of Sin: Find the Equation from the Original Curve

Read the original sine graph to determine its amplitude and period, then check the equation against its intercepts and turning points.

Question

The supplied graph represents a function of the form y=Asin⁡(Bx)y=A\sin(Bx) or y=Acos⁡(Bx)y=A\cos(Bx), with B>0B>0. Determine its equation.

Use the original graph below. The horizontal coordinates are in radians.

Original OpenStax exercise 163 graph: a sine curve through the origin, with trough at (-2,-4) and crest at (2,4)

Original figure: OpenStax, Calculus Volume 1, section 1.3, exercise 163.

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Evidence boundary

This solution uses the actual OpenStax section 1.3 exercise 163 image, including its marked axes and turning points. It determines the equation within the stated unshifted sine-or-cosine family with B > 0; it does not infer coordinates from an unrelated or reconstructed graph.