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

Express your answer in scientific notation. PLS HELP

Answers

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

hope this helps!

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)

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Answer:

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

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

Answers

The last option becuz math hero told me

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 )

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 :)

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]

84/120 equivalent fraction

Answers

Answer:

7/10

this should work

Step-by-step explanation:

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:

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

Good night, can someone please help me?

Answers

I Think Operation A is write

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.

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

Answers

B = 180-31

B = 149

Answer: 149

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

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)

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

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.

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 <...

122 is what percent of 145?

Answers

Answer:

84.1379%

Step-by-step explanation:

122 / 145 = 0.841379

(0.841379)(100) = 84.1379%

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

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.

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:

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.

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]

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

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:

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

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

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%

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

Answers

Answer:

$50.00 is the discount price

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