What angle does the tangent to the curve y(x)=sin^2 (x/4)+12sin(x/4) at x=4π make with the x-axis?
Express your answer to 3 significant figures. Choose the smaller angle, i.e., your answer should be positive and less than 90 degrees.

Question

What angle does the tangent to the curve y(x)=sin^2 (x/4)+12sin(x/4) at x=4π make with the x-axis?
Express your answer to 3 significant figures. Choose the smaller angle, i.e., your answer should be positive and less than 90 degrees.

ranga · Answer

Find dy/dx and put x = 4pi.  That will be the slope of the tangent to the curve at x = 4pi.  The angle will be the arctan (or tan inverse) of the slope.

anonymous · Answer

i got 3  but its wrong...

ranga · Answer

did you get 3 for the slope or the angle?

anonymous · Answer

the slope

ranga · Answer

They want the angle.  So take arctan(3) or tan inverse of 3.

Also find out if they want the angle in radians or degrees and set your calculator accordingly.

anonymous · Answer

Oh !!!!!! yea Tan^(-1)(3) is 71.6 degree and its  correct!!!!
thx

ranga · Answer

Cool.  yw.