Question

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

Answer 1

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

Explanation:

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

God bless....I hope the explanation is useful.