Answer:
y -2sin(12) = 4cos(12)(x -6)
Step-by-step explanation:
You want the tangent to y = 2·sin(2x) at x=6.
Slope
The slope of the tangent line at the point will be the derivative there.
y' = 2(2cos(2x)) = 4cos(2x)
y' = 4cos(12) . . . . . at x=6
Tangent point
The point of tangency will be the point on the given curve at x=6:
(6, 2sin(12))
Point-slope equation
Then the tangent line's equation can be written in point-slope form as ...
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -2sin(12) = 4cos(12)(x -6) . . . . . equation of tangent line
y -1.073 = 3.375(x -6) . . . . . . . approximate tangent line
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