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June 3rd, 2011, 11:37 PM   #1
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Radians?

I'm having trouble with this problem:

Find the gradient of y = 3sin2t + 4cos2t when t = 2.

It also tells me to use radians, although it was never explained to me so I really don't know how to apply them. Can someone please help me to understand?
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June 4th, 2011, 01:30 PM   #2
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Re: Radians?

Since you need to take derivatives, the derivative of sin x is cos x and the derivative of cos x is -sin x, WHEN x IS IN RADIANS.
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June 4th, 2011, 03:29 PM   #3
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June 4th, 2011, 10:08 PM   #4
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Re: Radians?

I know that much, but if I do 6cos4 - 8sin4 on a calculator I get roughly 5.428 and the answer is 2.133. The only thing I'm not doing is using radians, because I don't know where to use them or how to apply them to the situation.
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June 4th, 2011, 10:32 PM   #5
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Definition of radian: ?/180 = 1, e.g. ?/4 = (?/4)(180/?) = 180/4 deg = 45.
4 = k? ? k*3.14, hence k = 4/3.14. We'll use 4 ? 4?/3.14.
(4?/3.14)(180/?) = 720/3.14 deg ? 229.3, hence 6 cos 4 - 8 sin 4 ? 6 cos 229.3 - 8 sin 229.3 ? 2.15.
The given answer by you is 2.133, but 2.15 is close enough.
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June 5th, 2011, 12:28 AM   #6
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Re: Radians?

Thanks, I just tried this for myself and I've been getting the right answers. When trig functions are not involved is there any need/harm to use radians?
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June 5th, 2011, 01:07 PM   #7
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Re: Radians?

Quote:
Originally Posted by Phazon
Thanks, I just tried this for myself and I've been getting the right answers. When trig functions are not involved is there any need/harm to use radians?
Any time you do any mathematics requiring functions of angles (trig functions are the most common), you need to use radians.
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June 5th, 2011, 04:05 PM   #8
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See this.
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June 6th, 2011, 02:49 AM   #9
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Re: Radians?

Trig functions have many uses that have nothing to do with triangles and it is possible to define trig functions without using angles at all so that when you are asked to find sin(x) when x= 4 you don't have to worry about whether x is in degrees or radians just as you don't have to worry about units for x if you are asked to evaluate when x= 4. If you want to connect those with the trig functions you connect with right triangles, then you have to think "radians".
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June 6th, 2011, 03:12 PM   #10
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Re: Radians?

Quote:
Originally Posted by HallsofIvy
Trig functions have many uses that have nothing to do with triangles and it is possible to define trig functions without using angles at all so that when you are asked to find sin(x) when x= 4 you don't have to worry about whether x is in degrees or radians just as you don't have to worry about units for x if you are asked to evaluate when x= 4. If you want to connect those with the trig functions you connect with right triangles, then you have to think "radians".
This is very misleading. Sin(4) is quite different when 4 is radians than when 4 is degrees. Also, and more important, there are many areas, such as calculus, where trig functions are used and it is very messy to use anything but radians.
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