When do have have to put your calculator in radian mode? Sorry for the stupid question but this confuses me. B35tY Member. If the question is dealing with radians it won't have a degrees sign, and the angle will usually be in terms of pi , you would use radians in your calculations. Alternatively, sometimes you can just use degrees all the way through, and convert to radians at the end.
Do some prac questions, you'll see what i mean. Any other content, use radians, unless of course it says degrees. Be careful with sketches, they will give you either degrees or radians to use. In order to understand this, think about how we get the degrees. Take an angle with a fixed and a variable side. You can rotate the variable side until it completes a full circle. One degree is just that angle divided in equal shares.
The best analogy I can think of would be that between degrees and percentages. Both are just expressing proportions relative to a whole. Thus, you would expect the slopes derivatives to be much smaller than when working in radians. Pingback: What are Radians?
Where Do They Come From? Is this what you mean? With x in degrees you must change the argument to radians and then differentiate using the Chain Rule: This works the same way with any trig function. That is want I meant. Hi Lin, I like the way you have explained for easy understanding. However, please expalain or give reference of the inequality you have used for the explanation. Hi Ranjay I have added an explanation of the inequality at the end of the post. Thanks for writing; you were probably not the only one who was wondering about this.
Yes, if one were to use anything other than radian measure than one would get constants popping up upon differentiating trig functions and once they appeared these constants would mestasize. For the same reason one uses e as exponential base rather than the seemly more simple choice of say This must be nipped in the bud.
In elementary geometry where one is not using calculus the use of degrees or grads is perfectly OK. The radian is a linear measure of an angle, and it works best if you have your delta x and delta y in the same units. Degrees are a made up unit. Try plotting a sine wave using radians vs degrees for the x-axis. The y-axis will be the amplitude. A linear measurement. You are commenting using your WordPress. You are commenting using your Google account. You are commenting using your Twitter account.
You are commenting using your Facebook account. Notify me of new comments via email. Notify me of new posts via email. This site uses Akismet to reduce spam. Learn how your comment data is processed. To develop the derivative of the sine function you first work with this inequality At the request of a reader I have added an explanation of this inequality at the end of the post : From this inequality you determine that The middle term of the inequality is the area of a sector of a unit circle with central angles of radians.
Who needs that? Do your calculus in radians. Then the area of triangle OAB is 2. Like this: Like Loading It only takes a minute to sign up. Connect and share knowledge within a single location that is structured and easy to search.
How do I know when my calculator should be in radian or degree mode? Hopefully this makes sense I should mention that for those first 4 problems, I think the point is actually not to use a calculator. The technically correct thing to do is to assume that everything is in radians unless otherwise specified. However, humans tend to be bad at being technically correct, so if you haven't been told to use radians unless otherwise specified I would consider making contextual judgement calls. If you have been taught the technically correct rule, definitely use it.
This interpretation agrees with the rules of thumb that I am about to give everywhere that it's applicable, leaving the last problem. In contexts where you think your professor has simplified by opting to not use the degree symbol, some general rules of thumb can be applied. Another good rule of thumb is that if one interpretation gives an algebraic answer, use that interpretation.
0コメント