Question

Write the equation of the tangent line of y=2cosx at x=-pi/2??

Answer 1

to get equation of line, you'll need slope of tangent

slope of tangent at x = -pi/2
= y' at x = (-pi/2)

so first can you find the derivative of y ?

Answer 2

is the dervative of y=-sinx?

Answer 3

you mean \( y' = -2\sin x ?\)

Answer 4

then you just plug in x = -p/2 to get the slope
\(m= -2 \sin (\pi/2 )\)