Question

Find an equation for the line tangent to the graph of y=tan x at the point (pi/4, 1).

b) Find an equation for the line tangent to the graph of y=arc tan x at the point 9=(1, pi/4)

Answer 1

derivatives of tan x is sec^2(0)

Answer 2

slope = sec^2(1)

Answer 3

Part 1

Answer 4

Part 2

Answer 5

How do you know that sec^2(pi/4)=2?

Answer 6

sec x = 1/(cos x) So, sec^2 x = 1/cos^2 x
cos π/4 = 1/√2
cos^2 π/4 = 1/2
sec^2 π/4 = 2