Question

f′(0) if f(x)=sinx,

Answer 1

i think the answer is 0.017453 please check ??

Answer 2

0 = sinx is the equation, correct?

Answer 3

derivative of sin x is cos x
f'(0)= cos 0
f'(0)=1--> in degrees or in radians, same value

Answer 4

Actually, the values of radians and degrees are not the same. 1 radian = 180/pi to get the degree. So 1 radian equals approx. 57.3 degrees.

Answer 5

@skullofreak, are you wanting to convert 1 radian to degrees?

Answer 6

but in this case Θ=0°

Answer 7

Right, but the answer isn't 0 degrees..?

Answer 8

the answer for this is not an angle, when differentiating functions, it is simply looking for the tangent(slope or whatever you call it) at that specific point.
for the sine graph , it is asking what will be the slope at 0°

Answer 9

the variable "x" in the function is the degree

Answer 10

Okay I see what you're saying. Can it also be in degrees though? @skullofreak wanted degrees as an answer for some reason.

Answer 11

the value of the sin function is not in degrees or radians; it is a pure number, no units or dimensions.

Answer 12

the argument or input to the sin function IS in degrees, or radians (or gradians, which relatively few encounter: 400 gradians = 360 degrees).

Answer 13

actually the answer has to be rounded off to the 4th decimal... it cant be 360 degrees

Answer 14

i was thinking its pi/180 which = 0.017453... ???

Answer 15

well you want to know f prime of 0. so take the derivative of sinx and plug in 0.

Answer 16

But cos(0)=1 ain't in radians so you can't convert it into degrees?

Answer 17

no the answer is 1

Answer 18

if you want it in radians then it 2pi

Answer 19

derivative of sinx is cos x

Answer 20

how would i write 2pi in decimal form ?

Answer 21

6.2831853?..

Answer 22

nvm

Answer 23

Why would you write 2pi in decimal form?

Answer 24

umm... leave it in terms of pi or multiply 3.14 x 2

Answer 25

Slow down. The question asks what the value of the derivative of f(x)=sinx is at x=0. So since the derivative of sins is cosx, the question is asking what is cos(0). It doesn't matter whether you use radians or degrees because 0 radians = 0 degrees. The cos(0) is 1.

Answer 26

Wait I saw this question some time before...

Answer 27

I swear I saw the exact same question

Answer 28

type in 1 man.

Answer 29

There is no need to round. 1 is the exact answer. If you want 4 decimal places, write 1.0000.

Answer 30

i asked before but i was getting mixed answers and i have one try left so i want to be 100% sure cause im very confused :( @kc_kennylau

Answer 31

Or else the question is wrong

Answer 32

trust us

Answer 33

Don't care about how many tries you have with a wrong question

Answer 34

ok i will try 1.0000 then (its not 0.01745329 right 100%) ?

Answer 35

what on earth did you get that number from?

Answer 36

pi/180

Answer 37

Yes, where did that number come from?

Answer 38

but why?

Answer 39

It's 100% 1 (pun intended)

Answer 40

Why would you give that number? for f(x)=cos(x), x has no units therefore there is absolutely no need to do any conversion.

Answer 41

1.0000was wrong...

Answer 42

type in 1

Answer 43

it an exact value

Answer 44

Come on man, we discussed this before, I said the question was wrong; and I still so insist.

Answer 45

i cant anymore i got it wrong, but it needs to be a decimal rounded to the fourth decimall place

Answer 46

@kc_kennylau i emailed my teacher but he hasnt gotten back to me yet, so i needed to try other answers anyways

Answer 47

Well, then there's problem with the, uhm problem, because the exact answer is 1. I challenge you to use a calculator to calculate cos(0). It's 1. Always 1, an exact answer.

Answer 48

He tried 1 before

Answer 49

\[2\pi \approx 6.2832\] if you round

Answer 50

Why on earth are we talking about \(2\pi\)?

Answer 51

in radian. i use to do hw online on webassign and it doesnt tell you if it want it in term of pi or exact value

Answer 52

That's not the problem you gave us. That is a different problem. You need to enter progressively smaller values of h until the resulting answer doesn't change out to 4 decimal places. Doing as much yields an answer of 0.0174.

Answer 53

..... thats the same thing i got before and asked if it was correct....0.01745329251

Answer 54

which was pi/180 on the calculator :( damit... oh well.. thanks you guys

Answer 55

Well, the problem you gave us wasn't the problem as it was given to you. The difference quotient is only gives the exact answer for a derivative in the following case:\[f'(x)=\lim_{h \rightarrow 0}\frac{ f(x+h)-f(x) }{ h }\]

Answer 56

okay thank you i will let my teacher know, i was confused aswell and it doesnt give me the hint until after i get it wrong 4 times.thanks