Reviewing for Final and tying up some loose ends

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novicecrafter0608

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May 31, 2011
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Thank you in advance for taking the time to help me. I am working through some of the even problems in my text for definite integrals. While I can easily plug it into my ti-89 and check my work it does not provide step by step answers.My instructor does not allow calculators or notes on anything so I tend to get hung up on weird stuff. I do look up algebra mistakes etc. but sometimes I have no idea where to look for what I need to review! I will not doubt have a few more questions by the time this is done but for now:

The problem: [0,pi/3]S sin(4*angle) d(angle)

I have it worked out to

(-cos(4pi/3)/4) -(cos(o)/4)

now, I know what cos(pi/3) is and 4pi/3 is just a few quadrants away but how to I do it without a calculator? The answer is supposed to be sq root of 3 over 32. I do not understand how that could have happened regardless of what the first cos ends up being because I know the second one will be 1/4.

Thanks again!
 
You memorize the nature of 30-60-90 and 45-45-90 right triangles. If you meet pi/3 or pi/4 or pi/6 as reference angles, the sine or cosine of these values should come to mind without hesitation. What are your plans when your batteries expire?
 
I do know sin/cos of 30,60,45 but am not sure how to translate it to their counterparts in other quadrants. And I have been doing fine so far without a calculator- with a ton of work brushing up on skills but I do still get stumped sometimes!
 
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