1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
astra-53 [7]
3 years ago
11

Find the exact value by using a half-angle identity.cos five pi divided by twelve one divided by two times the square root of th

e quantity two plus the square root of three one divided by two times the square root of the quantity two minus the square root of three negative one divided by two times the square root of the quantity two plus the square root of three negative one divided by two times the square root of the quantity two minus the square root of three
Mathematics
1 answer:
love history [14]3 years ago
6 0

Answer:

+√[(2 - √3)/4]

Step-by-step explanation:

Here is the complete question

How do you find the exact values of cos(5pi/12) using the half angle formula?

Solution

The half-angle formula is

cos(θ/2) = ±√[(1 + cosθ)/2]

if cos(5π/12) = cos(θ/2) ⇒ θ/2 = 5π/12 ⇒ θ = 5π/6

So, θ = 5π/6 × 180/π = 150°

Cos150 = cos(180 - 30) = -cos30 = -cosπ/6 = -√3/2

So, cos(5π/12) = ±√[(1 + cos5π/6)/2]

= ±√[(1 + (-cosπ/6))/2]

= ±√[(1 - cosπ/6)/2]

= ±√[(1 - √3/2)/2]

= ±√[(2 - √3)/2 ÷ 2]

= ±√[(2 - √3)/4]

Since 5π/12 = 5π/12 × 180/π = 75° which is in the first quadrant, so

cos(5π/12) = +√[(2 - √3)/4]. We ignore the negative answer

You might be interested in
6х2 – 3х + 12 = ?<br> Gcf
natima [27]

Answer:

3(8-x)

Step-by-step explanation

6х2 – 3х + 12 = ?

= 12-3x+12

=24-3x

=3(8-x)

6 0
3 years ago
By the way need to show the work.
hammer [34]

Answer:

angle 2 is 85

Step-by-step explanation:

since its facing the 85

7 0
2 years ago
Read 2 more answers
I need help please!!
Aleksandr-060686 [28]

Answer:

1) Communism: government led by a single party often authoritarian.

2) Democracy: government that allows people to choose their leaders.

3) Socialism: government that owns goods and services. It encourages cooperation rather than competition.

4) Oligarchy: government of a few individuals usually wealthy, of certain race often authoritative rulers.

5) Monarchy: Government of one person that usually inherits it. Often inherited by gender. They can be constitutional with limited power or absolute, with unlimited power.

6) Theocracy: leader of a specific religion.

7) Totalitarianism: Government of one person without limitations of power.

8) Military Dictatorship: countries ruled by one person with absolute power.

Step-by-step explanation:

3 0
3 years ago
What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix? Enter the equation in the box.
antiseptic1488 [7]

Check the picture below.  So the parabola looks more or less like so.

let's recall that the vertex is half-way between the focus point and the directrix, at "p" units away from both.

Let's notice that the focus point is below the directrix, that means the parabola is vertical, namely the squared variable is the "x", and it also means that it's opening downwards as  you see in the picture, namely that "p" is negative, in this case "p" is 1 unit, and thus is -1.

\bf \textit{parabola vertex form with focus point distance} \\\\ \begin{array}{llll} 4p(x- h)=(y- k)^2 \\\\ \stackrel{\textit{we'll use this one}}{4p(y- k)=(x- h)^2} \end{array} \qquad \begin{array}{llll} vertex\ ( h, k)\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} h=-2\\ k=5\\ p=-1 \end{cases}\implies 4(-1)(y-5)=[x-(-2)]^2\implies -4(y-5)=(x+2)^2 \\\\\\ y-5=-\cfrac{1}{4}(x+2)^2\implies y=-\cfrac{1}{4}(x+2)^2+5

6 0
3 years ago
Is the square root of 16.45 a rational number or irrational number?
trapecia [35]

Answer:

Irrational

Step-by-step explanation:

The square root of 16.45 would be a number that will never end, making it irrational.

3 0
3 years ago
Read 2 more answers
Other questions:
  • (08.02)Which of the following graphs best represents the solution to the pair of equations below? y = x + 1
    6·2 answers
  • HELP!!! 15 points and marked brainliest
    6·1 answer
  • Matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on the lake is 42
    7·1 answer
  • Which question can be represented by the equation? Times 1/8 equals three
    6·1 answer
  • A piggy bank contains $2.40 in nickels and dimes. If there are 33 coins in all, how many nickels are there?
    14·1 answer
  • Convert 65 miles per hour to kilometers per hour. Use unit analysis to set up and solve.
    9·2 answers
  • Which statement about the following equations is correct? y=2x+5 y=−2x+5 Select one: a. The equations are dependent because the
    5·1 answer
  • 1/3 x 6/7=?<br> How do you multiply fractions?
    9·2 answers
  • Which statement is true?
    14·2 answers
  • Consider points R, S, and T.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!