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

[priscilla89]

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.

 

[tiny-tim]

hi priscilla89!

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

 

[priscilla89]

Ok thanks a lot.

- Happy Holidays

 

[madah12]

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.

 

[priscilla89]

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

0 = 0 + b

b= 0