Radian ConversionDate: 07/24/2012 at 11:00:45 From: Niras Subject: sin in radians I need -- NEED -- to brush up my skills in trigonometry, seriously. In calculating trig values, the sin of 30 degrees is .5. But with the calculator set to radians, sin(30) is now -0.988031624. Can you PLEASE show me the steps as to how? I know how to work with degrees, but tried to stay away from radians. Now it is inevitable, and I do not know how to do much calculating involving radians. But with your help, I believe I will eventually conquer it successfully. Date: 07/24/2012 at 11:20:35 From: Doctor Ian Subject: Re: sin in radians Hi Niras, You can think of degrees and radians as being like miles and kilometers. For example, if you are traveling 30 miles per hour, that's a different speed than 30 kilometers per hour -- even though the numbers are the same -- right? More to the point, suppose you have a circular track that is 2 miles around. If you start at point X and drive 30 miles, you end up where you started; you make 15 complete trips. But if you drive 30 kilometers, where will you end up? A kilometer is about 5/8 of a mile, so 5/8 mi 30 km * ------ = 150/8 mi, or 18 3/4 miles. 1 km So that would be 9 complete trips around, plus another 3/4 miles, or 3/8 of the way around the track. Make sense? In the same way, suppose you have an angle with a measure of 30 radians. Two pi radians takes you all the way around a circle (because the circumference is equal to twice pi times the radius). So two radians is equivalent to 360 degrees. That means 360 deg 30 rad * ------- = 1718.87 degrees 2pi rad That's four times around the circle, plus 278.87 degrees. So sin(30 rad) = sin(278.87 deg) = -0.988 Generally, when working with radians, it helps to keep a few key values in mind: 360 degrees = 2pi radians 180 degrees = pi radians 90 degrees = pi/2 radians 60 degres = pi/3 radians 45 degrees = pi/4 radians 30 degrees = pi/6 radians You can get those last four by dividing 180 degrees into 2, 3, 4, and 6 parts. In the same way, you could figure out that 36 degrees is pi/5, 15 degrees is pi/12, and so on. That's one of the nice things about 180 -- it has lots of divisors -- so you can make lots of exact fractions with it. Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ Date: 07/24/2012 at 12:00:20 From: Niras Subject: Thank you (sin in radians) Doctor Ian! Got it! Thank you! |
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