Understanding Sin 5Pi/12 and Converting to Degrees: Tips and Tricks"

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In summary, the conversation discusses finding the exact value of sin 5Pi/12 and different methods for approaching the problem. These include using addition and subtraction formulas, knowing exact values and identities, and using the half angle identity. The final answer for sin 5Pi/12 is (SQRT(6) + SQRT(2)) /4.
  • #1
powp
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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
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
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
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
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
Thanks. My problem is thinking which combnations would add up to 5pi/12
 

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