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

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:

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Answers

B = 180-31

B = 149

Answer: 149

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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%

122 is what percent of 145?

Answers

Answer:

84.1379%

Step-by-step explanation:

122 / 145 = 0.841379

(0.841379)(100) = 84.1379%

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

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]

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:

84/120 equivalent fraction

Answers

Answer:

7/10

this should work

Step-by-step explanation:

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

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.

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Answers

Answer:

See below

Step-by-step explanation:

Dilation is 1/2

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

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Answers

The last option becuz math hero told me

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Answers

Answer:

$50.00 is the discount price

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

358

Step-by-step explanation:

576

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Answers

πr²/2

22×7×7/7×2

77cm²

πr²/2×2

πr²

22/7×3.5×3.5

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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

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 :)

Good night, can someone please help me?

Answers

I Think Operation A is write

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

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.

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

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Answers

10^2=100
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hope this helps!

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
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Answer:

There ya go

Step-by-step explanation:

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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]

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 <...

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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 )

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:

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

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