- #1

- 91

- 0

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

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter powp
- Start date

- #1

- 91

- 0

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

- #2

AKG

Science Advisor

Homework Helper

- 2,565

- 4

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?How do I figure out what this is in degrees?

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

Homework Helper

- 2,440

- 138

5pi/12=75 degreespowp said:

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

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.

Last edited:

- #4

- 91

- 0

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

Homework Helper

- 2,440

- 138

that is rightpowp said:

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?

- #6

- 91

- 0

Thanks. My problem is thinking which combnations would add up to 5pi/12

Share:

- Replies
- 2

- Views
- 1K