exact value of tan 5pi/12

Answers

Answer 1

Answer:

[tex]\displaystyle \tan\frac{5\pi}{12}=2+\sqrt{3}[/tex]

Step-by-step explanation:

Tangent Half Angle

Given an angle θ, then:

[tex]\displaystyle \tan {\frac {\theta }{2}}=\frac {\sin \theta }{1+\cos \theta}[/tex]

We are required to find:

[tex]\tan\frac{5\pi}{12}[/tex]

But it cannot be found in tables of main angles. We can use the angle

[tex]\theta = \frac{5\pi}{6}[/tex]

And use the formula above to find the required operation. Hence:

[tex]\displaystyle \tan\frac{5\pi}{12}=\tan\frac{\frac{5\pi}{6}}{2}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac {\sin \frac{5\pi}{6} }{1+\cos \frac{5\pi}{6}}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac {\frac{1}{2} }{1-\frac{\sqrt{3}}{2}}[/tex]

Operating:

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac {\frac{1}{2} }{\frac{2-\sqrt{3}}{2}}[/tex]

Simplifying:

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{1}{2-\sqrt{3}}[/tex]

Rationalizing:

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{1}{2-\sqrt{3}}\cdot \frac{2+\sqrt{3}}{2+\sqrt{3}}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{2+\sqrt{3}}{2^2-\sqrt{3}^2}[/tex]

[tex]\displaystyle \tan\frac{5\pi}{12}=\frac{2+\sqrt{3}}{4-3}[/tex]

Finally:

[tex]\boxed{\displaystyle \tan\frac{5\pi}{12}=2+\sqrt{3}}[/tex]


Related Questions

What’s the constant of proportionality
(COP= constant of proportionality) help plz

Answers

It is the ratio between two directly proportional quantities.

Judy makes 2/5 of a beaded necklace on Monday she makes 3/10 of the necklace on Tuesday she makes 1/5 of the necklace on Wednesday what fraction of the necklace has Judy made so far

Answers

Answer: 9/10

Step-by-step explanation:

Fraction of beaded necklace made on Monday = 2/5

Fraction of beaded necklace made on Tuesday = 3/10

Fraction of beaded necklace made on Wednesday = 1/5

Total fraction made would be the addition of the Fractions made from Monday to Wednesday. This would be:

= 2/5 + 3/10 + 1/5

The lowest common multiple of the denominator is 10. Therefore we'll make them have a common denominator.

= 2/5 + 3/10 + 1/5

= 4/10 + 3/10 + 2/10

= 9/10

does someone know how to do this​

Answers

Answer:

us

Step-by-step explanation:

(B)

bbbbbbbbbbbbbbbbbbbbbbbbb

here is the questions sorry lol

Answers

Answer:

The first one is c, I’m pretty sure, the second one is a white block, and I don’t fully understand the last question but I’m pretty sure you’re correct

Step-by-step explanation:

Answer:

C. (0,-3)

Blank

D. (4,-5)

Step-by-step explanation:

(-1,-5)is point before translation (+1,+2)

(0,-3) after translation

Ok second one

90 degree counterclockwise rotation about the origin rule

A(x,y) becomes A'(-y,x)

n=(-5,-4) ok so -4 becomes positive 4

(4,-5)

Hope this helps!!

Simplify the expression given below.

X+2/x^3+2x^2-9x-18 divided by 3x+1 / x^2-9

A. 1 / (x+3)(x-3)
B. 3x +1
C. 1 / 3x+1
D. 3x + 1 / (x+3) (x-3)

Answers

Answer:

D

Step-by-step explanation: your welcome have a good day

Answer:

C.  [tex] \dfrac{1}{3x + 1} [/tex]

Step-by-step explanation:

[tex] \dfrac{x + 2}{x^3 + 2x^2 - 9x - 18} \div \dfrac{3x + 1}{x^2 - 9} = [/tex]

Factor all polynomials.

[tex] = \dfrac{x + 2}{x^2(x + 2) -9(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]

[tex] = \dfrac{x + 2}{(x^2 - 9)(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]

[tex] = \dfrac{x + 2}{(x + 3)(x - 3)(x + 2)} \div \dfrac{3x + 1}{(x + 3)(x - 3)} [/tex]

To divide by a fraction, multiply by its reciprocal.

[tex] = \dfrac{x + 2}{(x + 3)(x - 3)(x + 2)} \times \dfrac{(x + 3)(x - 3)}{3x + 1} [/tex]

Cancel out common factors in the numerator and denominator.

[tex] = \dfrac{1}{3x + 1} [/tex]

rearrange y= -3/4x + 2 in standard form with a positive lead to coefficient

Answers

Answer:

Step-by-step explanation:

    [tex]y=-\frac{3}{4} x+2\\add\frac{3}{4} x to both sides\\y+\frac{3}{4} x=-\frac{3}{4}x+\frac{3}{4} x+2\\y+\frac{3}{4}x=2\\\frac{3}{4} x+y=2[/tex]

Please mark me as brainliest!

Margaret is a waitress at The Seafood Bonanza. She earns $3 an hour plus 90% of her tips. Write an equation for her salary, S, if she works h hours and earns d dollars
in tips.

Answers

Answer: 3h + 0.9s

Step-by-step explanation:

90% is the same as 0.9 of..

Determine the value of x

Answers

Answer: 8


22 is to 11 because they are both on the hypotenuse. Since 11 is half of 22, x would be half of 16, 8.

Answer:

I would think it is 8

Step-by-step explanation:

By assuming the triangles are equal to each other in a way that the larger triangle is the smaller triangle's length times 2. For example, one side of the smaller triangle is 11 so times 2 would be the larger triangle's side. So, by dividing 16 by two, you would get 8. Hope this helped and that I did it correctly!

(GIVING BRAINLIEST!!!!!!)

Solve 1 ÷ 1/2 = ________

A) 2
B) 3
C) 4
D) 5

Answers

Answer:

B

Step-by-step explanation:

Becuase 1 divide 1/2

You make the division sign a multiplication sign

1 time 1/2

get the recipricol of 1/2 wich is 2

1 times 2/1

is 2

need a correct answer
A B C D E F

Answers

Answer:

B and D

F also has vertical angles however they haven't been numbered like the others

what is the answer to y=2x-9

Answers

Sorry to break it to you, but...

That's a line equation my dude. There's no answer.

Answer:

x=4.5 y=0

Step-by-step explanation:

For the x coordinate set y to zero for the y coordinate set x to zero. Example:

0=2x-9

9=2x

4.5=x

Name the solution........

Answers

Answer:

No solution

Step-by-step explanation:

here you go mate

step 1

3x+y=-3,3x+y=3  equation/solution

step 2

3x+y=-3  add -3x

y=-3x-3

step 3

3x+y=3  substitute and simplify

0=6

answer

no solution


Some one help please fast help ASAP

Answers

Answer: (x, y) --> (x, -y)

Step-by-step explanation:

This is a reflection over the x-axis so its only the y-intercept that changes.

Answer:

its a reflection

Step-by-step explanation:

If it were a rotation, it wouldnt have overlapped.

If it were a translation, It would have been the wrong way up and not overlapping.

When reflected over line x, it will overlap because it stays rigid and does not change shape or size.

hope this helps :)

He highest priced diamond ever sold at auction weighed 69.42 carats and sold for $1,050,000. A carat is equal to 0.2 grams. What was the weight of this diamond in grams?

Answers

Answer:

13.884 grams

Step-by-step explanation:

From the question:

1 carat = 0.2 grams

The highest priced diamond = 69.42 carats.

Hence:

1 carat = 0.2 grams

69.42 carats = x grams

x grams = 69.42 × 0.2 grams

x grams = 13.884 grams

Hence, the weight of the highest priced diamonds is 13.884 grams.

Multiply. Write your answer in simplest form 1/3 x 1/6

Answers

Answer:

1/18

Step-by-step explanation:

1 x 1 = 1

3 x 6 = 18

1/18

plz help me with math :)

Answers

Answer:

it would be 3 in the first box and 24 in the other

Step-by-step explanation:

because the ratio is 3 years to 24 montsh most of the time the larger number is on the left and the smaller number is on the right and 3 years is more than 24 months 24 months is only two years

If you invent something, you have ____

A commenced something

B devise something

C originated something

D discover something

Don’t answer if u don’t know

Answers

Answer:

here are the definitions of each..

Step-by-step explanation:

Commence: begin; start

Devise: plan or invent (a complex procedure, system, or mechanism) by careful thought.

Originated: create or initiate (something).

Discover:find (something or someone) unexpectedly or in the course of a search.

so it cant be A of D so it would have to be B of C but i think the best answer is C

Answer:

If you invent something, you have ____

the answer is

C)  originated something

The height of the roof will be 9 feet instead of 5 feet. Determine the length, in feet of the diagonal wood beams on the new roof. Find the leg. a^2 + 9^2=13^2

Answers

Answer:

√88

Step-by-step explanation:

a^2 + 9^2=13^2

a² = 13² - 9²

a² = 169 - 81

a² = 88

Take square root of both sides

a = √88

If y = -5, what is the value of
2y+2
-
4

Answers

Answer:

-12

Step-by-step explanation:

Ok so I'm guessing that's a -4 but if its not, please correct me.

y= -5 is going to be plugged into 2y+2-4

This means that 2(-5)+2-4=?

2(-5) is the equivalent to 2 times -5, which is -10 (you solve multiplication first because order of operations)

Now, 2-4=-2

So using this, let's combine both equations!

-10+-2=?

?=-12

It's a lot of steps but they get easier the more you do them <3

I don’t get this side of algebra need answer

Answers

Answer:

b

Step-by-step explanation:

FAST
Work out using calculator
a) 122
b) 142
c) 62
Find the square root of
a) 121
b) 900
c) 729

Answers

Answer:

Find square root

a 11×11

B 30×30

C 27×27

2 + 2 = ______________________________________________

Answers

Answer:4

Step-by-step

On a math exam containing 36 questions, there are
8 questions on geometry and 6 questions on
statistics. The other questions are on numeration.
Which part of the exam is on numeration?

Answers

Answer:

22

Step-by-step explanation:

If Lucy runs 1 2/3 miles each day, how many miles will Lucy run in 2 days?

Answers

Answer:

She will run 3 1/3 miles in 2 days

Step-by-step explanation:

1 2/3 + 1 2/3 = 2 4/3

= 3 1/3

Answer:

10/3 and mixed fraction is 3 1/3

Step-by-step explanation:

What is the range of the cluster in the scatter plot?

A: Between 4 and 8 years of experience
B: Between 6 and 12 years of experience
C: Between $10,000 and $60,000
D: Between $40,000 and $60,000

Answers

Answer:

b

Step-by-step explanation:

answer :


b


hope this helped

Combining Like Terms
1. 10Z-4B+3Z+16B-Z

2. -5M-3P+5P+12P

3. 12P-4M+8P-3M-2P

4. 10B-5M-4B+8B-4M

5. 4Z+3Z-6Z+B

6. 7B+3X-8B+6X

(By the way Those letters without a number by it, is 1. So EX: 4Z+5+Z is 5Z+5 ) ​

Answers

Step-by-step explanation:

1. 10Z–4B+3Z+16B–Z = 10Z+3Z–Z+16B–4B

= 12Z+12B = 12(Z+B)

2. –5M–3P+5P+12P = 12P+5P–3P–5M = 14P–5M

3. 12P–4M+8P–3M–2P = 12P+8P–2P–4M–3M

= 18P–7M

4. 10B–5M–4B+8B–4M = 10B+8B–4B–5M–4M

= 14B–9M

5. 4Z+3Z–6Z+B = Z+B

6. 7B+3X–8B+6X = 6X+3X+7B–8B = 9X–B

What is the measure of /GMH
A 40°
B 45°
C 50°
D 90°

Answers

Answer: A

Step-by-step explanation: /GMK is a right angle and /HMK is 50 degrees so 90-50=40

A is the answer because 90-50

the girl boy ratio was 9-7 if 63 girls attended how many boys attended?

Answers

Answer:

49      100 percnet

Step-by-step explanation:

9:7

times by 7

The number of boys attended are 49.

What is the definition of the ratio?In mathematics, a ratio is a term used to compare two numbers. It is used to express how large or small an amount is in comparison to another. A ratio compares two quantities by dividing them. The dividend is referred to as the 'antecedent,' while the divisor is referred to as the 'consequent.'

For the given question.

Let the number of girls be 'x' = 63.

Let the number of boys be 'y'.

The ratio of girls to boy is 9:7.

Thus,

x/y = 9/7

Boys  = ?

y = 7x/9

Put x = 63

y = 7×63/9

y = 49

Thus, the number of boys attended are 49.

To know more about the ratio, here

https://brainly.com/question/12024093

#SPJ2

4) Find the measure of the third angle.*
10 points
B
10 mm
540
5.9 mm
?
A
8.1 mm
60
35
36

Answers

Answer:

36

Step-by-step explanation:

angle A + angle B + angle C= 180°

180=90+54+angle A

angle A = 36

Answer:

b??? I think I'm so sorry if this is wrong I tried

Solve for V.
3y=39
Simplify your answer as much as possible.

Answers

Answer:

3y=39 :3

y=13

Step-by-step explanation:

prove me wrong

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