Author Question: How to find the derivative of trig functions? (Read 1494 times)

camila

  • Hero Member
  • *****
  • Posts: 705
How would you find the derivative of sin(x), i know the answer but I don't know how you would derive the answer. I don't want it worked out the whole way but if you could just tell me the steps I need to take that would be great.
And are the other trig functions derived the same way?
Thanks!



TI

  • Sr. Member
  • ****
  • Posts: 434
(1) You want to find the limit of the following expression (E) as h -->0:

E = [sin(x + h) - sin(x)]/h

(2) For this, expand sin(x + h) to obtain:

sin(x + h) = sin(x)cos(h) + cos(x)sin(h)

(3) Now, as h -->0, cos(h) -->1 and sin(h) -->h

so... as h --> 0

(4) E --> [sin(x) + h cos(x) - sin(x)]/h = h cos(x)/h = cos(x)

Hence, the derivative of sin(x) = cos(x)

-----------------------------------------
The derivatives of other basic trig functions can be derived

the same way.






Related Topics

Need homework help now?

Ask unlimited questions for free

Ask a Question

camila

  • Hero Member
  • *****
  • Posts: 705
GOLD :D Thanks so much!!



 

Did you know?

Cucumber slices relieve headaches by tightening blood vessels, reducing blood flow to the area, and relieving pressure.

Did you know?

Drug abusers experience the following scenario: The pleasure given by their drug (or drugs) of choice is so strong that it is difficult to eradicate even after years of staying away from the substances involved. Certain triggers may cause a drug abuser to relapse. Research shows that long-term drug abuse results in significant changes in brain function that persist long after an individual stops using drugs. It is most important to realize that the same is true of not just illegal substances but alcohol and tobacco as well.

Did you know?

Bacteria have been found alive in a lake buried one half mile under ice in Antarctica.

Did you know?

Aspirin may benefit 11 different cancers, including those of the colon, pancreas, lungs, prostate, breasts, and leukemia.

Did you know?

Every flu season is different, and even healthy people can get extremely sick from the flu, as well as spread it to others. The flu season can begin as early as October and last as late as May. Every person over six months of age should get an annual flu vaccine. The vaccine cannot cause you to get influenza, but in some seasons, may not be completely able to prevent you from acquiring influenza due to changes in causative viruses. The viruses in the flu shot are killed—there is no way they can give you the flu. Minor side effects include soreness, redness, or swelling where the shot was given. It is possible to develop a slight fever, and body aches, but these are simply signs that the body is responding to the vaccine and making itself ready to fight off the influenza virus should you come in contact with it.

For a complete list of videos, visit our video library