How do you find the tangent to y = cos x at x = pi/2?

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Answer 1 · 2016-07-05T15:02:00

Tangent line $color(blue)(y=-x+pi/2)$

given $y=cos x$

Find the point of tangency first

$y=cos (pi/2)=0$

The point $(x_1, y_1)=(pi/2, 0)$

Solve for the slope $m$ using the first derivative of $y=cos x$

$y' = d/dx(cos x)=-sin x$

$m=-sin (pi/2)=-1$

Use now the point-slope form

$y-y_1=m(x-x_1)$

$y-0=-1(x-pi/2)$

$y=-x+pi/2$

Kindly see the graph for better analysis of the solution
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