Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (π, 0)?

Solution:

In geometry, the tangent line (or tangent) means a line or plane that intersects a curved line or surface at exactly one point. 

Given:

y = sin(sin(x))

By chain rule we get,

y' = cos (sin x) × cos x

When x = π

y'(π) = cos (sin π) × cos π

So we get,

y’(π) = cos (0) × (-1)

y’(π) = -1

We know that the equation of a tangent is

y - y₁ = m (x - x₁)

Substituting the values

y - 0 = - 1(x - π)

y = -x + π

y = π - x

Therefore, the equation of the tangent line is y = π - x.

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Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (π, 0)?

Summary:

An equation of the tangent line to the curve at the given point y = sin(sin(x)), (π, 0) is y = π - x.