Answer:
- m = √3 ≈ 1.7321
- b = 1 -π√3/6 ≈ 0.0931
Explanation:
You want the slope-intercept form equation for the tangent line at point (π/6, 1) on the curve y = 2·sin(x).
Slope
The slope of the line at the point of tangency is the derivative of the curve at that point:
y' = 2cos(x) = 2·cos(π/6) = 2(√3/2)
m = √3 . . . . . approximately 1.7321
Y-intercept
Solving the line's equation for b, we have ...
y = mx +b
b = y -mx = 1 -(√3)(π/6)
b = 1 -π√3/6 . . . . . approximately 0.0931
Equation
The equation of the line is ...
y = mx +b
y = (√3)x +1 -(π√3)/6