What Does the Tangent Line at x=0 Reveal About y=sin(x)?

priscilla89
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Homework Statement



Find an equation of the tangent line to y = sin x at the point x = 0. Graph both functions on the same set of axes on the interval [-pie/4, pie/4]. What does this illustrate?

Homework Equations



y = mx + b

The Attempt at a Solution



y = sin x ---> y' = cos x

y = cos (0) = 1


y = mx + b
0 = 1 (0) + b
0 = b

y = x + 0

I'm wondering if I am on the right track. Any help will be appreciated, thanks a lot.
 
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hi priscilla89! :wink:

yes that's right … the tangent line is y = x :smile:
 


Ok thanks a lot.

- Happy Holidays
 


you meant y=sin(0) right? because the point is (x,f(x)) not (x,f'(x)) but it seems you corrected it when you found the equation of the line so I think it's ok.
 


Right it would've to be y = sin (0) = 0. Basically it would be then

0 = 0 + b

b= 0
 
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