Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

1 answer:

5 0

Hello:
Use implicit differentiation : y sin 12x = x cos 2y
y' sin12x+12ycos12x =cos2y -2x y'sin2y
when : x = π/2 and y =π/4

y' sin12(π/2) +12(π/4)cos12(π/2) =cos2(π/4) -2(π/2) y'sin2(π/4)
y' sin(π/6) +(π/3)cos(π/6) =cos(π/2) - π y'sin(π/2)

y' (1/2) +(π/3)(√3/2) = - π

y' (1/2) =-(π/3)(√3/2) - π
y' = -π (1+√3)/3
an equation of the tangent line is : y- π/4 = ( -π (1+√3)/3)(x-π/2)

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Explanation:

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since FT = TH, we know that FT is half as long as FH; or put another way, FH is twice as long as FT.

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Extra info

* Segment HS is an angle bisector: it cuts angle GHF in half.

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