Question

Use the function defined below to find an equation of the tangent line at the point indicated.

y=sinx, x=pie/3

Answer 1

i have my slope of the tangent = root3/2

Answer 2

hey again

y' = cos(x)
y'(pie/3) = cos(pie/3) = 1/2

Answer 3

so thats my slope

Answer 4

yes.. 1/2 is the slope

Answer 5

now use
y=y1+m(x-x1)
in order to find the tangent line

Answer 6

is my point (pie/3, sin(1/2)) ??

Answer 7

no.. (pie/3,sin(pie/3))

Answer 8

and we should write pi :P

Answer 9

i need to write it in the form y=

Answer 10

use this ..
now you have a point (x1,y1) and a slope m
y=y1+m(x-x1)

Answer 11

\[y-\sin \frac{ \pi }{ 3 }=\frac{ 1 }{ 2 }x-\frac{ \pi }{ 6 }\]

Answer 12

good..

Answer 13

Sin(pi/3) = sqrt(3)/2

Answer 14

so you can arrange it as :
y(x) = x/2 +sqrt(3)/2 - Pi/6
or
y(x) = x/2 + (3sqrt(3)-Pi)/6

Answer 15

thx

Answer 16

yw