Tangent to r = 1 + sin(θ) at θ = π/6

Calculus 2 · Axiom Academy

Find the tangent line to a polar curve at a specific point using the polar slope formula. Find the equation of the tangent line to the polar curve at . We will compute r and r' at the angle, locate the point, then use the polar slope formula . The cardioid . At the curve reaches its rightmost edge, so the tangent there is the vertical line . Nice work! You found the tangent line to a polar curve from start to finish. The moves that got us there: Differentiate r(θ): here , the derivative of . Convert to Cartesian: , give the point . Apply the polar slope formula: the numerator is but the denominator is 0 , so the slope is undefined. Read the geometry: an undefined slope means a vertical tangent — the line is . This recipe works for any polar curve. Watch the denominator: when it hits 0 the tangent is vertical, and when the numerator hits 0 instead it is horizontal.

This is the written version of the interactive lesson above. See the full Calculus 2 course.