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

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 )

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Answer:

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Answer:

$50.00 is the discount price

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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

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:

122 is what percent of 145?

Answers

Answer:

84.1379%

Step-by-step explanation:

122 / 145 = 0.841379

(0.841379)(100) = 84.1379%

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:

There ya go

Step-by-step explanation:

Express your answer in scientific notation. PLS HELP

Answers

10^2=100
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Answers

I Think Operation A is write

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!! ( write a rule to describe each transformation)

Answers

Answer:

See below

Step-by-step explanation:

Dilation is 1/2

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

Answers

B = 180-31

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Answer: 149

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]

Which is the equation of a circle with a radius of 6 and a center of (3,-1)?
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Answers

Answer:

358

Step-by-step explanation:

576

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Answer:

7/10

this should work

Step-by-step explanation:

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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

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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

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]

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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

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

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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.

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%

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FAST FASTTTT

Answers

Answer:

Step-by-step explanation:

56 would be ya answer

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 <...

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]

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Answers

Answer:

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

Step-by-step explanation:

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Answers

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

Answer: 39

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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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