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Mila [183]
3 years ago
7

The equations of the tangent to the curve y=xsinx at the point (pi/2,pi/2) is

Advanced Placement (AP)
1 answer:
never [62]3 years ago
8 0
The first thing you have to realize is that tangent is the slope of a curve on a given point. You can solve for the slope by finding the derivative of the given function. So:

\frac{d}{dx} xsin(x)

Next use product rule (I recommend watching videos if you're confused):

= [sin(x)] + [x*cos(x)]

Next substitute you x-value (π/2) into your derivative:

= [sin(  \frac{ \pi}{2} )] +[ \frac{\pi}{2}*cos( \frac{\pi}{2})]
= 1 +  \frac{\pi}{2} *0
= 1

So our slope at π/2 is 1. Next we use our slope-form and substitute our given value and solve for y-intercept (algebra-stuff) 

( \frac{\pi}{2}) =  1( \frac{\pi}{2}) + b
b = 0

So we get our equation:

y = x

So our answer is E

Feel free to ask any questions.
Hopes this helps!
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