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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:
Next use product rule (I recommend watching videos if you're confused):
![= [sin(x)] + [x*cos(x)]](https://tex.z-dn.net/?f=%3D%20%5Bsin%28x%29%5D%20%2B%20%5Bx%2Acos%28x%29%5D)
Next substitute you x-value (π/2) into your derivative:
![= [sin( \frac{ \pi}{2} )] +[ \frac{\pi}{2}*cos( \frac{\pi}{2})]](https://tex.z-dn.net/?f=%3D%20%5Bsin%28%20%20%5Cfrac%7B%20%5Cpi%7D%7B2%7D%20%29%5D%20%2B%5B%20%5Cfrac%7B%5Cpi%7D%7B2%7D%2Acos%28%20%5Cfrac%7B%5Cpi%7D%7B2%7D%29%5D%20%20)
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)
So we get our equation:
So our answer is E
Feel free to ask any questions.
Hopes this helps!
Next use product rule (I recommend watching videos if you're confused):
Next substitute you x-value (π/2) into your derivative:
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)
So we get our equation:
So our answer is E
Feel free to ask any questions.
Hopes this helps!