mathsolver
  • mathsolver
Prove that d/dx sin(x)=cos(x) iff the period of sin(x)=2pi
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
DebbieG
  • DebbieG
Find \[\large \frac{ d }{dx }\sin(bx)\] Which will involve the chain rule and be a function of b. What must b= in order for that that derivative to =cos(x)? When b= that, what is the period of sin(bx)?
mathsolver
  • mathsolver
d/dx sin(bx)=bcos(bx) therefore b=1
DebbieG
  • DebbieG
Right, any other value for b and the derivative is not =cos(x). Although, any other value for b, and you aren't taking the derivative of sin(x), lol... you would take taking the derivative of sin(bx) which is not =sin(x) if b is not=1. So it seems like a bit of an oddly worded problem. :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

mathsolver
  • mathsolver
What I mean is why do we use radians for trigonometric functions. I know it means we don't have to mess around with coefficients when we differentiate. But how do we know it's radians that has this nice property
DebbieG
  • DebbieG
Gosh, I'm sorry, I guess I don't really understand what you're asking. But my simplistic answer would be, we use radians because radians are just real numbers, and hence all the properties and operations we apply to them can be carried out without any kind of conversions....? Don't ask "why use radians", ask, "why NOT use radians?" ;) lol
mathsolver
  • mathsolver
Haha, yeah, fair enough. I just want to know how we know that radians have this lovely property but degrees don't
DebbieG
  • DebbieG
The property being that \(\large \dfrac{ d }{dx }\sin(x)=\cos(x)\)?

Looking for something else?

Not the answer you are looking for? Search for more explanations.