How can I use the result of sin(PI/8) to find the cos and sin of other angles?

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In summary, the conversation discusses finding the angles 5PI/8, 9PI/8, 13PI/8, and 17PI/8 from a complex equation problem and using the result of sin(PI/8) to find the values of sin and cos for these angles. The individual mentions using standard trigonometry identities and finding formulas for cos(5x) and cos(17x), but expresses difficulty in doing so. They then realize that 17PI/8 is equal to 2PI + PI/8 and are able to find the values for cos and sin using this knowledge.
  • #1
sony
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I have (from a complex equation problem) found the following angles in the answers:

5PI/8, 9PI/8, 13PI/8, 17PI/8

In the same assignement I found sin(PI/8) = .5*sqrt(2-sqrt(2)) and I found the cos(PI/8) value by using standard trig. identities.

Is there an easy way to use this result to find the cos and sin of the angles stated? (The assignement tells us to use the answer we found from sin(PI/8))

I know I can find formulas for cos(5x) etc by using this method: http://library.thinkquest.org/C0110248/trigonometry/form3.htm

But that is going to take ages up to cos(17x) !

I think I've missed something here.

Thanks
 
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  • #2
Hmm.. 5/8-1/8=1/2, I think. And 17=16+1, if I'm not mistaken
 
  • #3
I'm not getting it... :P
 
  • #4
[tex]\frac{17\pi}{8}=\frac{16\pi}{8}+\frac{1\pi}{8}=2\pi+\frac{\pi}{8}[/tex]
For example
 
  • #5
ah, thanks I get it!
 

1. What is the value of cos(8) in the denominator?

The value of cos(8) in the denominator is approximately 0.9902.

2. How is cos(x): 8 in x's denominator related to trigonometric functions?

Cos(x): 8 in x's denominator is a specific expression that involves the cosine function, which is a trigonometric function used to calculate the ratio of the adjacent side to the hypotenuse in a right triangle. In this expression, the number 8 is being used as the value for x in the denominator.

3. Is cos(x): 8 in x's denominator a common mathematical expression?

No, cos(x): 8 in x's denominator is not a common mathematical expression. It is a specific expression that may be used in a mathematical problem or equation.

4. How can cos(x): 8 in x's denominator be simplified?

Cos(x): 8 in x's denominator can be simplified by using a trigonometric identity, such as the reciprocal identity, to transform it into a more recognizable form. For example, cos(x): 8 in x's denominator can be simplified to 1: 8sec(x).

5. What is the significance of using cos(x): 8 in x's denominator in a mathematical problem?

The use of cos(x): 8 in x's denominator in a mathematical problem signifies that the value of x is important in determining the overall value of the expression. It may also indicate the presence of trigonometric functions and the need for trigonometric principles to be applied in solving the problem.

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