Find the equation of the normal line to a trigonometric curve at a given point by evaluating its derivative.

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Equation of the Normal Line to a Cosine Curve

Trigonometric and inverse trigonometric functions warmup

Find an equation of the normal line to the curve \( y = 1 + \cos x \) at the point \( (\pi/3, 3/2) \).

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What you need first

Derivatives of basic trigonometric functions
Evaluating trigonometric functions at standard angles
The relationship between the slopes of perpendicular lines
Point-slope form of a linear equation

What this problem tests

Tests the ability to differentiate a trigonometric function, evaluate it at a specific angle, find the perpendicular slope, and write the equation of a line.

This is a standard introductory calculus problem testing the geometric interpretation of the derivative and basic trigonometric differentiation.

Equation of the Normal Line to a Cosine Curve

What you need first

What this problem tests

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