Vault Of Euclid

Proving Tangency for a Trigonometric Curve

Trigonometric and inverse trigonometric functions core

Show that the curve $y=x \sin x$ is tangent to the line $y=x$ whenever $x=(4 n+1)(\pi / 2)$, where $n$ is any integer.
derivativesproduct-ruletangent-linetrigonometric-functionsperiodicitysinecosineprove-tangencycalculus-i

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What this problem tests

Tests the ability to apply the product rule, evaluate trigonometric functions at periodic intervals, and understand the geometric conditions for tangency.

This problem is typical in a first-semester calculus course when learning the product rule and derivatives of trigonometric functions.

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