Find out the answer to "How do you find the equation of the..."

Beckham Short

Answered question

2022-04-14

How do you find the equation of the line tangent to

y = 4 \cos x

x = \frac{π}{6}

Ferrito90gn

Beginner2022-04-15Added 12 answers

The equation of the tangent at

x = \frac{π}{6}

for

y = 4 \cdot \cos x

y - y (\frac{π}{6}) = y^{'} (\frac{π}{6}) (x - \frac{π}{6})

where

y (\frac{π}{6}) = 4 \cdot \cos (\frac{π}{6}) = 4 \cdot \frac{\sqrt{3}}{2} = 2 \cdot \sqrt{3}

and

y^{'} (x) = - 4 \cdot \sin x

and

y^{'} (\frac{π}{6}) = - 4 \sin (\frac{π}{6}) = - 4 \cdot \frac{1}{2} = - 2

Hence we have that

y - 2 \cdot \sqrt{3} = - 2 \cdot (x - \frac{π}{6}) \Rightarrow y = - 2 x + \frac{π}{3} + 2 \cdot \sqrt{3}

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