How do you figure out

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Hello All

I have this question that I have to find the exact value of sin 5Pi/12. How do I figure out what this is in degrees? Or how do I break this down so I can use addition or subtraction foumulas?

Thanks
 

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  • #2
AKG
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How do I figure out what this is in degrees?
How to figure out what 5pi/12 is in degrees? Are you learning from a textbook or teacher, or are you learning on your own? I have to assume that you know how to answer this question. What do you know so far about radians?

sin(10pi/12) = 2sin(5pi/12)cos(5pi/12) = 2sin(5p/12)SQRT[1 - sin(5pi/12)]

sin(10pi/12)/2 = sin(5p/12)SQRT[1 - sin(5pi/12)]

0.5/2 = sin(5p/12)SQRT[1 - sin(5pi/12)]

You should know that sin(10pi/12) = sin(5pi/6) = sin(pi/6) = 0.5

1/16 = sin²(5p/12) - sin³(5pi/12)

16x³ - 16x² + 1 = 0, where x = sin(5pi/12)

There's a way to factor cubics, but I don't remember it. However, if you look it up on the internet, or even search these forums, you can easily find a method. Once you've factored it, the roots of the equation will naturally be your answer. Note that you might get up to 3 roots, but should only get one that is in [0, 0.5]. Can you tell why the root in that interval will be your answer?
 
  • #3
lurflurf
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powp said:
Hello All

I have this question that I have to find the exact value of sin 5Pi/12. How do I figure out what this is in degrees? Or how do I break this down so I can use addition or subtraction foumulas?

Thanks
5pi/12=75 degrees
pi=180 degrees
What exact values do you know? What identities do you know? The standard exact values to know are pi/10 and pi/12 if you knew them and multiples you would know 5pi/12. you could use the half angle identity to write sin(5pi/12) in terms of cos(5pi/6). You can learn the values for pi/6 and pi/3 by noting pi/3+pi/6=pi/2 and sin(pi/2)=1 cos(pi/2)=0. Also 5pi/6=pi-pi/6. Also don't try to factor a cubic, it would work, but it is difficult and unnecisary.
 
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  • #4
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Thanks for the responses

I am going to use pi/4 and pi/6 and plug it into SIN(pi/4 + pi/6). This should give me the exatct value. The answer I get is (SQRT(6) + SQRT(2)) /4

Is this correct?
 
  • #5
lurflurf
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powp said:
Thanks for the responses

I am going to use pi/4 and pi/6 and plug it into SIN(pi/4 + pi/6). This should give me the exatct value. The answer I get is (SQRT(6) + SQRT(2)) /4

Is this correct?
that is right
 
  • #6
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Thanks. My problem is thinking which combnations would add up to 5pi/12
 

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