Trig Distributive Problem

Jason76

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\(\displaystyle (\dfrac{\pi }{8})[[4 \cos \dfrac{\pi }{8}] + [4 \cos \dfrac{\pi }{4}] + [4 \cos \dfrac{3\pi }{8}]] + [4 \cos \dfrac{\pi }{2}]\) :confused: What does this come out to?

My attempt:

\(\displaystyle (\dfrac{\pi }{8})[[4 (.9238795325)] + [4(.70710678118)] + [4(.38268343236)] + [4(0)]]\)
 
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\(\displaystyle (\dfrac{\pi }{8})[[4 \cos \dfrac{\pi }{8}] + [4 \cos \dfrac{\pi }{4}] + [4 \cos \dfrac{3\pi }{8}]] + [4 \cos \dfrac{\pi }{2}]\) :confused: What does this come out to?
What do you mean by "come out to"?

What generated this expression? What are you supposed to be doing with it?
 
You know you can factor that "4" in each term out don't you? Are you not asked for exact values? Otherwise this just becomes an exercise in using a calculator! (Surely you know how to add using a calculator!?)

You should know that \(\displaystyle cos(\pi/4)= -\sqrt{2}/2\).

\(\displaystyle cos(\pi/8)\) is a little harder: the "half angle" formula says that \(\displaystyle cos(x/2)= \sqrt{1+ cos(x)}/2\) so so \(\displaystyle cos(\pi/8)= \sqrt{1+ cos(\pi/4)}/2\)\(\displaystyle = \sqrt{1+ \sqrt{2}/2}/2\). Similarly, \(\displaystyle cos(3\pi/8)= cos(\pi/4)cos(\pi/8)- sin(\pi/4)sin(\pi/8)\)
 
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Same as:
\(\displaystyle (\dfrac{\pi }{2})[[cos \dfrac{\pi }{8}] + [cos \dfrac{\pi }{4}] + [cos \dfrac{3\pi }{8}]] + [cos \dfrac{\pi }{2}]\)

Are you sure the "]]" is properly positioned? Should it be at the end?

Since \(\displaystyle [cos \dfrac{\pi }{2}] \ = \ 0\) - the "numerical" answer is not affected.
 
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Actually this is a right triangle approximation problem (the final step of the problem).

But the computer probably won't accept decimal answers, preferring something from the unit circle. But some of these values like \(\displaystyle \cos \dfrac{3\pi}{8}\) and \(\displaystyle \cos\dfrac{\pi}{8}\) come out to weird non-decimal values, as well as strange decimal ones. These have to be multiplied to \(\displaystyle \dfrac{\pi}{8}\)

I guess there is no other way but just to calculate it out, but probably the computer won't accept the answer.
 
Looked again, the computer (from watching the help video) wants us to go decimal. So the mistake might be not using the right amount of digits or something.
 
Actually this is a right triangle approximation problem (the final step of the problem).
As has been mentioned elsewhere, it would be extremely helpful if you would begin to include the actual exercise and its instructions, rather than continuing to require us to guess. :roll:
 
Looked again, the computer (from watching the help video) wants us to go decimal. So the mistake might be not using the right amount of digits or something.

That is just ridiculous that the computer wants decimal answers. Do they even say to what decimal value you are to round your answer too? And if you round your answers within the calculation that can change your final answer in the end. Shame on the computer folks for wanting a decimal answer.
 
Doing decimal approximations isn't that hard (from what I saw on the video example). You can find the Cos or Sin etc.. of any radian value by typing it into google like this: sin(pi/8) etc..

Just round it to 4 digits. and you got it. I haven't figured out my calculator too much, so I have to use the decimal value (without rounding) of a radian value (assuming were not taking the trig function of it). You do this by simply dividing the top and the bottom (either of which might contain pi, which in that case you would use the full decimal value for it).
 
Doing decimal approximations isn't that hard (from what I saw on the video example). You can find the Cos or Sin etc.. of any radian value by typing it into google like this: sin(pi/8) etc..

Just round it to 4 digits. and you got it. I haven't figured out my calculator too much, so I have to use the decimal value (without rounding) of a radian value (assuming were not taking the trig function of it). You do this by simply dividing the top and the bottom (either of which might contain pi, which in that case you would use the full decimal value for it).

Thanks! I was wondering how to exactly use this contraption called a calculator. Phew, now I can solve all these problems I have in front of me. :rolleyes:
 
Have moved these problems to the Calculus section, as they were just one part of various "endpoint rectangle integration" problems.
 
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