Find an equation of the tangent line to the curve at the given point. y=secx (pi/3,2)
1 answer:
To get the equation of tangent, we need a point on it and its slope.
we already have (x1,y1) = (pi/3,2) on the tangent line.
To get the slope of tangent,
m = derivative of y at the given point.
y = sec x
y' = sec x tan x
at x = pi/3,
y' = sec pi/3 tan pi/3
y'= 2
so the slope of tangent is 2
equation will be
y -y1 = m (x-x1)
y - 2 = 2 (x- pi/3)
Thats your equation of tangent.
you can simplify if you want.
we already have (x1,y1) = (pi/3,2) on the tangent line.
To get the slope of tangent,
m = derivative of y at the given point.
y = sec x
y' = sec x tan x
at x = pi/3,
y' = sec pi/3 tan pi/3
y'= 2
so the slope of tangent is 2
equation will be
y -y1 = m (x-x1)
y - 2 = 2
Thats your equation of tangent.
you can simplify if you want.
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