Help me find the equation

Question

help me find the equation for the tangent line for the function y=3sin(4x) at =pi/4

thank you, please show as many steps as possible to help me understand.

Answer 1

Point on tangent line = (π/4, sin[4(π/4)]) = (π/4, 0)

Slope of tangent line is the derivative of y = sin(4x) evaluated at x = π/4 (the derivative of sin(4x) is 4cos(4x))

So, slope = 4cos[4(π/4)] = -4

Using the point slope form, equation of tangent line is y - 0 = -4(x - π/4).

Simplify to get y = -4x + π.