Author Topic: applications of derivatives of circular functions question (Read 719 times) Tweet Share

aakritisharma · « **on:** July 09, 2013, 03:28:35 pm »

hey.

im having some problems with a question

q. find the acute angle of intersection of the curves y=sin2x and y=cosx at the point (pi/2,0)

thanks

SocialRhubarb · « **Reply #1 on:** July 09, 2013, 10:53:10 pm »

OK, firstly, what you're finding is the angle between the tangents of the two curves at that point.

To find tangents we need to find their derivatives.

Spoiler

$y_1=\sin(2x)$

$\frac{dy_1}{dx}=2\cos(2x)=2\cos(\pi)=-2$

$y_2=\cos(x)$

$\frac{dy_2}{dx}=-\sin(x)=-\sin(\frac{\pi}{2})=-1$

$\tan(\theta)=\frac{Opposite}{Adjacent}=\frac{rise}{run}=\ gradient$

$\theta_1=\arctan(-2)\approx -1.11\ radians$

$\theta_2=\arctan(-1)\approx -0.785\ radians$

The angle between the two functions at that point is the difference between those two angles.

$\theta\approx 0.322$

aakritisharma · « **Reply #2 on:** July 10, 2013, 03:27:38 pm »

thank you so much

I GET IT. i suck at angles lol

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