Find the exact value of tan /12.

Find the exact value of tan π/12.

Answers

Answer 1

[tex]\textit{Half-Angle Identities}\qquad tan\left(\cfrac{\theta}{2}\right)= \begin{cases} \pm \sqrt{\cfrac{1-cos(\theta)}{1+cos(\theta)}} \\\\ \cfrac{sin(\theta)}{1+cos(\theta)}~~\leftarrow \textit{let's use this one} \\\\ \cfrac{1-cos(\theta)}{sin(\theta)} \end{cases} \\\\\\ 2\cdot \cfrac{\pi }{12}\implies \cfrac{\pi }{6}~\hspace{10em} \cfrac{~~ \frac{\pi }{6}~~}{2}\implies \cfrac{\pi }{6}\cdot \cfrac{1}{2}\implies \cfrac{\pi }{12}[/tex]

so let's use the double of the angle in the half-angle identities, check the picture below for the cosine, sine pairs

[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{sin\left( \frac{\pi }{6} \right)}{1+cos\left( \frac{\pi }{6} \right)}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{1+\frac{\sqrt{3}}{2}}[/tex]

[tex]tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{~~ \frac{1}{2}~~}{~~\frac{2+\sqrt{3}}{2}~~}\implies tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2}\cdot \cfrac{2}{2+\sqrt{3}} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill tan\left( \cfrac{~~ \frac{\pi }{6}~~}{2} \right)=\cfrac{1}{2+\sqrt{3}}~\hfill[/tex]

Related Questions

Which function has a greater rate of change?

Answers

Answer:

Function A

Step-by-step explanation:

In function A as x increases by 1, y increases by 5.

In function B there is a slope of -4.5 which means as x increases by 1, y increases by -4.5.

Rate of change of 5 is greater than a rate of change of -4.5.

A group of friends were working on a student film that had a budget of $1300. They used $546 of their budget on props. What percentage of their total budget did they spend on props?

Answers

To find percentage: divide the given value by the total and multiply by 100

546/1300 x 100 = 42%

Question
Which of the following angle measures are possible for a triangle to be classified as acute? Select all that apply.
Select all that apply:
45°, 34", 101°
122, 36, 22
75°, 61°, 44°
22°, 86°, 72

Answers

Answer:

45°, 75°, 61°, 44°, 22°, 86°

Step-by-step explanation:

They have to be angles less than 90°.

Answer:

(d) 22°, 86°, 72

Step-by-step explanation:

The largest angle must be less than 90°, and the sum of angles must be 180°. These conditions are met by the lists of angles shown above.

Express your answer in scientific notation. PLS HELP

Answers

10^2=100
3600-6.3-100= 3493.7

hope this helps!

A 6pint bucket of paint costs $28.44 what is the price per cup

Answers

Answer:

I think there answer is 4.74

Step-by-step explanation:

so you divide

[tex]6 \div 28.44 \: and \: you \: get \: answer[/tex]

Simple interest ending balance $41,900 at 4% for 2 years?

Answers

Answer:

The simple interest is $3352.

Step-by-step explanation:

Using PRT/100, we can find the interest.

=> 41,900 x 4 x 2/100 => 419 x 4 x 2=> $3352Conclusion:

Therefore, the simple interest is $3352.

Hoped this helped.

[tex]BrainiacUser1357[/tex]

Pls help i neeed to get my grade up badly

Answers

Step-by-step explanation:

12 - 1/2r = ( 13 - 3/2r ) - ( 1 - r )

r - 13/6 = ( 7r - 3/2 ) - ( 2/3 + 6r )

13r + 20 = ( 6r + 7 ) + ( 13 + 7r )

-12 + r = ( -8 - r ) + ( 2r - 4 )

During a chess match there are 15 pieces left on the board. the ratio of the white pieces to black pieces is 3 : 2 how many white pieces are on the white board?

Answers

Answer: 9

==========================================================

Explanation:

The ratio 3:2 scales up to 3x:2x for some positive whole number x.

We have 3x white pieces, 2x black pieces, and 3x+2x = 5x pieces total. Set this equal to the 15 mentioned and solve for x.

5x = 15

5x/5 = 15/5

x = 3

Therefore, there are 3x = 3*3 = 9 white pieces and 2x = 2*3 = 6 black pieces, which gives 9+6 = 15 total. The ratio 9:6 reduces to 3:2 after dividing both parts by the GCF 3.

Rebecca draws a graph of a real-world relationship that turns out to be a set of unconnected points. Can the relationship be linear? Can it be proportional? Complete the explanation of your reasoning.

Answers

Answer:

Step-by-step explanation:

II
Homework: Secti...
Question 2, 7.1.5
>
Find the critical value Za/2 that corresponds to the given confidence level.
95%
.....
za/2
(Round to two decimal places as needed.)
(

Answers

Answer:

2.17

Answer and Explanation:

The critical value of z for 97% confidence interval is 2.17, which is obtained by using a z score table, that is: {eq}P(-2.17 < Z <...

LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)

Answers

Answer:

See below

Step-by-step explanation:

Dilation is 1/2

U (2, 3) U' (1, 1.5)

V (1, -2) V' (0.5, -1)

pls answer pls plsplspls pls

Answers

πr²/2

22×7×7/7×2

77cm²

πr²/2×2

πr²

22/7×3.5×3.5

38.5cm²

77-38.5=38.5cm²

Find the values of sin, cosine, and tangent, for

Answers

A B=5
sin=3/5
cos=4/5
tan=3/4

[tex]sin = \frac{opposite}{hypotenuse} = \frac{3}{5} = 0.6\\\\cos = \frac{adjacent}{hypotenuse} = \frac{4}{5} = 0.66666666666666666666666666666667\\\\tan = \frac{opposite}{adjacent} = \frac{3}{4} = 0.75\\\\hypotenuse = 5[/tex]

HOPE THIS HELPS :)

For what value(s) of k is + 3 a factor of 3 + 5 2 + − 9
FAST FASTTTT

Answers

Answer:

Step-by-step explanation:

56 would be ya answer

Which is the equation of a circle with a radius of 6 and a center of (3,-1)?
(x - 3)2 + (y+1)2 = 36
(x+3)2 + (y - 1)2 = 36
(x+3)2 + (y - 1)2 = 6
(x-3)2 + (y+ 1)2 = 6

Answers

Answer:

358

Step-by-step explanation:

576

3] If the p.d.f., of the random variable X is given by

f(x)= K/sqrt x &0 otherwise

(c) P(|X| < 3)

(d) E(2X - 2)

(e) V(3X)

Answers

Answer:

PDF for a continuous random variable is given. Use the PDF to find (a) and the CDF.

84/120 equivalent fraction

Answers

Answer:

7/10

this should work

Step-by-step explanation:

Find the circumference of a circle with a radius of 8 mm.

Answers

Answer:

C=50.27mm

Step-by-step explanation:

C=2πr=2·π·8≈50.26548mm

Find the center and radius of the circle with the equation: (x=5)2 +(4-2)3-25

Answers

Answer:

center = (5 ,-3) and radius = 5

Step-by-step explanation:

Kelly base 3328 cookies each year she bakes twice as many cookies in October then in the other much how many cookies does Kelly back in December

Answers

256 Cookies
There are 12 months and twice the amount of cookies in one month is equal to an extra month. So do 3328/13=256.

shirt original price is $100 and is now 50% off what is the discount price now

Answers

Answer:

$50.00 is the discount price

Good night, can someone please help me?

Answers

I Think Operation A is write

122 is what percent of 145?

Answers

Answer:

84.1379%

Step-by-step explanation:

122 / 145 = 0.841379

(0.841379)(100) = 84.1379%

If answer is correct I will mark as brainliest.
which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?

5x^3+x^2-7x+28=0

A. Zero

B. Two or Zero

C. One

D. Three or one

Answers

Answer:

No positive real solutions.So the answer is zero.

Step-by-step explanation:

LAST ATTEMPT MARKING AS BRAINLIEST!! (Graph the image of the figure using the dilation given)

Answers

Answer:

There ya go

Step-by-step explanation:

Solve for x; x: 6 = 54: 162 A. 1 B. 2 C. 3 D. 4
find x

Answers

Answer:

x = 2

Step-by-step explanation:

x:6 = 54:162

What is 54 to 162?

162/54 = 3.

So x times 3 should equal 6.

6/3 = 2.

x = 2

Let's confirm,

2:6 = 54:162

Answer:

8 - 10

8 + 10

Step-by-step explanation:

edmentum/plato

URGENT PLEASE HELP simplify (3^8 / 3^5)^3

Answers

The last option becuz math hero told me

the difference of 3 times a number and 18 is 39 what is the number

Answers

The answer is 13 because if you divide 39 by 3 you will get your answer.

Answer: 39

(3*(19))-18 = 39

57-18 = 39 we have the correct answer

Tracy bought a can of yellow paint to use on the table and chairs in her backyard. She used 1.25 liters of paint on the chairs. She has less than 3 liters of paint left for the table.

Answers

The inequality that describes the given problem is x - 1.25 < 3.

The given parameters:

Number of paints used on the chair, = 1.25 LitersNumber of paints left for the table, less than 3 liters

Let the number of liters in one can of yellow paint = x

The following inequality can be used to represent the liters of paint left for the table.

the liters of paint left = x - 1.25

The liters of paint left is less than 3 liters;

x - 1.25 < 3

Thus, the inequality that describes the given problem is x - 1.25 < 3.

The missing part of the question is below:

Write the inequality that describes the given problem

Learn more about word problem of inequality: https://brainly.com/question/1194852

Examine the figure. What is the measure of angle b?

Answers

B = 180-31

B = 149

Answer: 149

Other Questions

The session delivered the information I expected to receive. *A.Strongly AgreeB.AgreeC.NeutralD.DisagreeE.Strongly Disagree:) What is the domain and range of this? Is it a function yes or no? Solve for x. 7/8 = x/16 Why does Iceland have geothermal energy? The mongol conquests of much of Eurasia in the thirteenth century tended to encourage trade along the silk roads primarily by A) opening large new markets for both european and east asian goods in central asiaB)increasing the demand or military supplies needed by the mongol armies that occupied various regionsC)decreasing the risk of bandit attacks and reducing the number of local rulers collecting tribute from trade caravans D)discouraging seaborne trade along the Indian Ocean routes that competed with the silk roads It is possible to use a decision making process for any decision. Please select the best answer from the choices provided T F. Imagine that a future historian is writing about the erayou live in now. Which objects do you think thehistorian would most likely write about to show thefreedom people today enjoy? Read the excerpt from "Music Gets Personal. Radios had to be made and sold. Radio stations had to be built, too. All of this took more time. Finally, in the 1920s, music recording and radio came together. People listened to music in their homes. They bought record players. They listened to music on the radio, too. What is the best summary of this excerpt? Many people held jobs making and selling radios and building radio stations and record players. Families enjoyed listening to music and other shows that were broadcast on the radio. In the 1920s people became interested in purchasing records so they could play them on their record players. Radio created a music industry, and by the 1920s people began enjoying music at home. In a collision, a 30 kg ball moving at 3 m/s transfers all of its momentum to a 5kg ball. what is the velocity of the 3kg ball after the collision? What did people previously believe about the movements of Sun and Earth? explain the term global south what is 110/12- 28/12 as an improper fraction CAN SOMEONE HELP ME PLEASE ASAP!? Basic steps in Research Process Fe3+ and S2- write the formula for the compound that would be formed Light intensity (I) is proportional (a) to the inverse square of distance (d) of a subject from a lightsource. The relationship in intensities for subjects at different distances from the same source canbe likewise seen as a ratio or proportional relationship.I xA proportional relationship can be mathematically expressed as follows for light intensity (I) inlumens when a subject is at the light source.Lumens at current distanceLumens at origin or sourceSo, if a light intensity (I) is 516 lumens at the source and 4 lumens at a specific distance from thesource, what is that distance?Round the value to the nearest tenth if necessary. You do not need to include a label for distance.Only the number, rounded to the tenth, will be necessary. Triangle ABC has coordinates A(6,2), B(3,6), and C(5,0). Find the perimeter of the triangle. Round your answer to the hundredths place (2 decimal places) I will give brainliest Students who are awardedback.for college do not have to pay the moneyO A. loansO B. feesO C. their first choice of dormsD. grants if a is more than b, what is the equation for an ellipse with a centre at the origin and a horizontal major axis? f(-3)f(x)= 3 to the power of x