### How JustAnswer Works:

• Ask an Expert
• Get a Professional Answer
• 100% Satisfaction Guarantee

Ryan, Engineer
Category: Pre-Calculus
Satisfied Customers: 7826
Experience:  B.S. in Civil Engineering
40260889
Type Your Pre-Calculus Question Here...
Ryan is online now

# Find the exact value of cos pi/12 using half angle identity. simplify,including

### Resolved Question:

Find the exact value of cos pi/12 using half angle identity.
simplify,including any radicals. Use integers or fractions for any numbers in the expression.Rationalize all denominators.
Submitted: 2 years ago.
Category: Pre-Calculus
Expert:  Ryan replied 2 years ago.
Hi,

Thank you for using JustAnswer.

The half-angle identity for cosine is:

cos(a/2) = ±√(1 + cos a)/2

Using this:

cos(pi/12) = cos (pi/6 / 2) = ±√(1 + cos pi/6)/2 = ±√(1 + √3/2)/2 = ±√(1/2 + √3/4)

cos(pi/12) = ±√(2+√3) / √4

cos(pi/12) = ±(1/2)√(2+√3)

cos(pi/12) ≈ 0.9659

Please let me know if you need to match a specific answer choice like some of yesterday's problems.

Thanks,

Ryan
Customer: replied 2 years ago.
which is the final answer?
Expert:  Ryan replied 2 years ago.
Hi,

That depends on if they are asking for a value or an expression.

If they want a value, then it is 0.9659, when rounded to four decimal places.

If they want an expression, then it could be ±√((1 + cos pi/6) / 2). In this case though, it would be helpful to see the answer choices that are available (if it is multiple choice).

Thanks,

Ryan
Customer: replied 2 years ago.
here is an example they game me with the answer.

sin 7pi/12 = sqrt 2 + sqrt3/2
Expert:  Ryan replied 2 years ago.
Hi,

The answer for cos(pi/12) happens to be the same as the answer for sin(7pi/12).

It looks like this:

(The computer program might not care about the ± sign though...)

Thanks,

Ryan
Ryan, Engineer
Category: Pre-Calculus
Satisfied Customers: 7826
Experience: B.S. in Civil Engineering
Ryan and other Pre-Calculus Specialists are ready to help you

### JustAnswer in the News:

Ask-a-doc Web sites: If you've got a quick question, you can try to get an answer from sites that say they have various specialists on hand to give quick answers... Justanswer.com.
JustAnswer.com...has seen a spike since October in legal questions from readers about layoffs, unemployment and severance.
Web sites like justanswer.com/legal
...leave nothing to chance.
Traffic on JustAnswer rose 14 percent...and had nearly 400,000 page views in 30 days...inquiries related to stress, high blood pressure, drinking and heart pain jumped 33 percent.
Tory Johnson, GMA Workplace Contributor, discusses work-from-home jobs, such as JustAnswer in which verified Experts answer people’s questions.
I will tell you that...the things you have to go through to be an Expert are quite rigorous.

### What Customers are Saying:

• Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
< Last | Next >
• Wonderful service, prompt, efficient, and accurate. Couldn't have asked for more. I cannot thank you enough for your help. Mary C. Freshfield, Liverpool, UK
• This expert is wonderful. They truly know what they are talking about, and they actually care about you. They really helped put my nerves at ease. Thank you so much!!!! Alex Los Angeles, CA
• Thank you for all your help. It is nice to know that this service is here for people like myself, who need answers fast and are not sure who to consult. GP Hesperia, CA
• I couldn't be more satisfied! This is the site I will always come to when I need a second opinion. Justin Kernersville, NC
• Just let me say that this encounter has been entirely professional and most helpful. I liked that I could ask additional questions and get answered in a very short turn around. Esther Woodstock, NY
• Thank you so much for taking your time and knowledge to support my concerns. Not only did you answer my questions, you even took it a step further with replying with more pertinent information I needed to know. Robin Elkton, Maryland
• He answered my question promptly and gave me accurate, detailed information. If all of your experts are half as good, you have a great thing going here. Diane Dallas, TX

• ### Mr. Gregory White

#### Satisfied Customers:

153
M.A., M.S. Education / Educational Administration
< Last | Next >

### Mr. Gregory White

#### Satisfied Customers:

153
M.A., M.S. Education / Educational Administration

### Ray Atkinson

#### Satisfied Customers:

43
Inner-city high school substitute teacher. Degrees in mathemetics, accounting, and education. Years and years of tutoring.

### mhasan420

#### Satisfied Customers:

37
BA Maths, Oxford

### JACUSTOMER-yrynbdjl-

#### Satisfied Customers:

13
I have taught college Mathematics for the past 10 years.

### Martin

#### Satisfied Customers:

44
20+ years of research, engineering and teaching

### manas11

#### Satisfied Customers:

12
Tutor & Engineer
• /img/opt/shirt.png Math-John's Avatar

### Math-John

#### Satisfied Customers:

211
MS and BS in Math.

Chat Now With A Tutor
Ryan
633 Satisfied Customers
B.S. in Civil Engineering