Question

Use differentials (or equivalently, a linear approximation) to approximate sin(44)as follows: Let f(x)=sin(x) and find the equation of the tangent line to f(x) at a "nice" point near 44 degrees. Then use this to approximate sin(44) .

Answer 1

this is a bunch of hogwash, although no doubt it is what your math teacher wants

Answer 2

this is a bunch of hogwash, although no doubt it is what your math teacher wants

Answer 3

so whats the answer? i tried what imranmeah said and didnt get the right answer

Answer 4

whatever he said i don't know, but tell your math teacher that the derivative of sine is NOT cosine if you are working in degrees!

Answer 5

you could use linear approximation to find the sine of a number near
\[\frac{\pi}{4}\] using calculus, but not 44 degrees!

Answer 6

how about sin(45)?

Answer 7

trig functions are functions of numbers, not of degrees. they correspond to the usual functions of angles only if your are measuring angles in radians, not in degrees. so this makes no sense whatsoever

Answer 8

it is true that IF you are working in degrees then certainly
\[\sin(45)=\frac{\sqrt{2}}{2}\]

Answer 9

but you cannot take the derivative and and get cosine. that is just plain wrong.

Answer 10

the whole problem is stupid. sorry. you can look here to see what i mean. the idea is you are supposed to find the equation of the line tangent to the graph. the point is
\[(45,\frac{\sqrt{2}}{2})\] but you cannot find the slope there by taking the derivative, because the derivative of sine is cosine as functions of numbers, not as functions of "degrees"

Answer 11

cannot find the slope by saying that the derivative of sine is cosine because it is not

Answer 12

ask your math teacher how you are supposed to find the slope of the line tangent to the graph of
\[y=\sin(x)\] at x = 45 degrees. if he or she tell you that you take the derivative and replace x by 45 degrees make sure they he or she knows that the derivative of sine is not cosine when working as a function of degrees. so you cannot, i repeat cannot do it this way

Answer 13

alright man ill let him know, thanks for helping me tonight i will be on tomorrow probably, i gotta roll

Answer 14

it can of course be done. if you are working in degrees then the derivative of sine is
\[\sin'(x) = \frac{π}{180}\cos(\frac{πx}{180})\]

Answer 15

i doubt you were expected to know that however.
yw