Equation of Tangent Line

Question

1.) y= 4 sin x at x = 9

2.)y= 8 tan x at x = 6

Answer 1

y = 4 sin x

y' = 4 cos x

M = 4 cos 9

B = y - mx

= f(9) - (4 cos 9)(9)

= 4 sin 9 - 36 cos 9

y = mx + b = (4cos9) x + (4 sin9 - 36 cos9)

= (4 cos 9) [ x + 4 sin9 - 9 cos 9]

= (4 cos 9) [ x + ( 4 sin 9 - 9 cos 9)]

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y = 8 tan x

f(6) = 8 tan 6

m = f'(6) = 8 (sec 6)^2

B = y - mx = 8 tan 6 - 8 (sec 6)^2 (6)

= 8 tan 6 - 48 (Sec 6)^2

y = mx + b = 8 (sec 6)^2 x + 8 tan 6 - 48 (Sec 6)^2

y = 8 ( sec 6)^2 [ x + 8 tan 6 - 6 ]