Find the equation of the tangent line to the curve y=6sinx at the point (π/6,3

1 answer:

6 0

Hello:
f(x) =6sin(x)
f'(x) = 6 cos(x)

the equation of the tangent line is : y=f'(π/6)(x-π/6)+f(π/6)
f'(π/6)=6cos(π/6)=6×(√3/2)=3√3
f(π/6) =3
the equation is : y = 3√3(x-π/6)+3

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see the attachments for the two solutions

Step-by-step explanation:

When the given angle is opposite the shorter of the given sides, there will generally be two solutions. The exception is the case where the triangle is a right triangle (the ratio of the given sides is equal to the sine of the given angle). If the given angle is opposite the longer of the given sides, there is only one solution.

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