Homework Help

Find an equation of the tangent line to the curve   y=sin(3x)+cos(2x) at the...

user profile pic

masterpiece56 | Student | (Level 1) Honors

Posted March 21, 2012 at 1:44 PM via web

dislike 2 like

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=

 

1 Answer | Add Yours

user profile pic

cosinusix | College Teacher | (Level 3) Assistant Educator

Posted March 21, 2012 at 2:05 PM (Answer #1)

dislike 1 like

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`

 

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes