Question

Find the equation of the tangent line to the curve y=6sin(x) at the point (pi/6, 3). the equation of this line can be written in the form y=mx b m=b=

Answer 1

The equation will be:
y=mx+b;
m=slope
b=y-intercept

1) we have to calculate the slope
a) we find the first derivative of the function:
y=6sin(x)
y´=6 cos(x)

b) we find "m" at the point π/6
m=f´(π/6)=6 cos (π/6)=6(√3)/2=3√3.

2)We find the equation of the tangent line at (π/6, 3).
a) we need to find y-intercept (b).
slope-point form of a line:
y=mx+b

Data:
x=π/6
y=3
m=3√3

Therefore:
3=3√3(π/6)+b
3=(π√3)/2+b
b=3-(π√3)/2=(6-π√3)/2

Therefore, the equation of this line would be:
y=(3√3)x+(6-π√3)/2

Answer:      y=(3√3)x+(6-π√3)/2