Find an equation of the tangent line to the curve   y=sin(3x)+cos(2x) at the point(pi/6, y(pi/6)). Tangent line: y=  

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cosinusix | College Teacher | (Level 3) Assistant Educator

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The slope of the tangent line is given by the derivative.

`y'(x)=3cos(3x)-2sin(2x)`

`y'(pi/6)=3cos(pi/2)-2sin(pi/3)`

`y'(pi/6)=0-sqrt(3)`

 

`y(pi/6)=sin(pi/2)+cos(pi/3)=3/2`

 

An equation of the tangent line at `x=pi/6` is `y=y'(pi/6)(x-pi/6)+y(pi/6)`

Answer: `y=-sqrt(3)(x-pi/6)+3/2`

 

 

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