Question

Find the equation of the tangent line to the curve y=6secx−12cosx at the point (π/3,6). The equation of this tangent line can be written in the form y=mx+b where

Answer 1

i get how to get m but not b

Answer 2

b is the point where line crosses the y-axis (where x = 0)

Answer 3

i know that but dont know how to find it

Answer 4

what is the slope?

Answer 5

use the form y-y1 = m(x-x1)

where m = slope , x1 =pi/3 and y1 = 6

and rearrangge to y = mx + b

Answer 6

y-6=(6 (cos(2 x)+2) tan(x) sec(x))(x-(pi/3)

Answer 7

confused on where i go from here

Answer 8

y = ( 6(cos(2 x)+2) tan(x) sec(x)) * x - [6 (cos(2 x)+2) tan(x) sec(x))*(pi/3)] - 6

Answer 9

oopps + 6 at the end

Answer 10

we can simplify the 'b' a little

- 6 [ (cos(2 x)+2) tan(x) sec(x))(pi/3) - 1]