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]

Find The Exact Value Of Tan /12.

Related Questions

1plss help, its time

Answers

Answer:

60 degrees

Step-by-step explanation:

Similar shapes have the same angles but different side lengths.

Answer:

The answer is 60°

Step-by-step explanation:

Because pentagon JKLMN is basically the same as pentagon VWXYZ and if you see in the smaller pentagon the angle for L is 90° and same goes for the bigger pentagon

I need help with this solve

Answers

Answer:

the answer is 64%

Step-by-step explanation:

80/125 = 64

What is the value of the expression 2z ÷ [z – (z – 4)] when z = 8?

Answers

2z ÷ [z – (z – 4)]

Sub z=8 into the expression

2(8) ÷ [8 – (8 – 4)] = 16 ÷ 4

                             = 4

Ivanna is saving money to buy a game. So far she has saved $12, which is 3/4 of the total cost of the game. How much does the game cost?​

Answers

Answer:

24?

Step-by-step explanation:

sabihin nyo kung mali -_-

Harry is riding a train that goes 70 miles an
hour. How far will he travel is 3.5 hours?

Answers

Answer: 245 miles

Step-by-step explanation:

(70)(3.5)= 245

Harry will travel 24.5 miles

(70) (3.5) = 24.5

help me plssssssssssssssssssssss

Answers

Answer:

p < 319

Step-by-step explanation:

1/5 of 400 showing work

Answers

1/5 of 400 = 80
400 x 1/5 = 400/5
400/5 = 80

Save You More offers a buy one/get one free item each week. Customers who purchase only one of the items must pay the regular
price. The limit is one deal per customer. Is the relation (# sale items purchased, price) a function? Why or why not?

A)
B
It is a function because the input can be either 1 or 2 items, but the output
will always be the same price.
It is not a function because the input can be either 1 or 2 items, but the
output will always be the same price.
It is a function because the input will always be the same price, but the
output can be either one or two items.
D
It is not a function because the input will always be the same price, but the
output can be either one or two items.

Answers

Answer:

It is a function because the input can be either 1 or 2 items, but the output

will always be the same price.

Step-by-step explanation:

Answer:

A. It is a function because the input can be either 1 or 2 items, but the output

will always be the same price.

Step by Step Explanation :

A function is for every single input but the output is always the same. So, let's make a scenario. If someone bought ' 1 ' then paid the marked cost and if you bought 2 then paid the marked cost BUT with " One Buy One Free. " So, it is in fact a function.

Don’t know where to start

Answers

Answer:

A = 80π

Step-by-step explanation:

Area of a circle is A = πr²

Area of the the largest circle - Area of the smaller circle = the shaded part.

Largest circle    -    Area of the smaller circle   = Shaded part of circle

A  = π(12)²         -     A = π(8)²

    144π            -      64π                           =        80π

Tyler is saving to buy a new videogame system. For every $15 he earns mowing lawns, he saves $9. On Saturday, Tyler earned $105 mowing lawns. How much money did he save?

Answers

Answer:

$63

Step-by-step explanation:

First, we find the percentage that he saves:

9 is 3/5 of 15 which is 60%, 9 is 60% of 15 which means he save 60% of the money that he earns so,

60% of 105 = 63

This means he saved $65 from the money he earned.

Hope this helps!

I need help with this answer PLEASE I’m stuck

Answers

Answer:

40% of airline A's flights were on time

Step-by-step explanation:

0.4=40% .the top row indicates that it was airline A. the left column indicates that it was on time.

Answer:

B

Step-by-step explanation:

happy holidays

Help help math math math math

Answers

y=2/1+7 is the answer because it’s a positive slope and i you go up by 2 spaces first then to the right by 1

Answer:

y=2/1+7

Step-by-step explanation:

Could someone help me solve this please? With explanation? ​

Answers

Answer:

x=109 degrees

Step-by-step explanation:

By alternate interior angles, the measure of angle ADE is the same as that of EAB, both of which are 38.

Because ADE is an isosceles triangle, the measure angle EAD is equal to that angle EDA; let that measure be x.

Because the angles of a triangle add up to 180, x+x+38=180 -> 2x+38=180 -> 2x=142 -> x=71

That means that angle EDA is 180 degrees

Because x is supplementary to angle EDA, the measure of angle x is 180-71=109 degrees

Ok done. Thank to me :>

2+6i/2-4i = a + bi What is the value of a? What is the value of b?

Answers

[tex]\dfrac{2+6i}{2-4i}\\\\\\=\dfrac{2(1+3i)}{2(1-2i)}\\\\\\=\dfrac{1+3i}{1-2i}\\\\\\=\dfrac{(1+3i)(1+2i)}{(1-2i)(1+2i)}\\\\\\=\dfrac{1+2i+3i+6i^2}{1-(2i)^2}\\\\\\=\dfrac{1+5i-6}{1+4}~~~~;[i^2=-1]\\\\\\=\dfrac{5i-5}{5}\\\\\\=\dfrac{5(i-1)}5\\\\=i-1\\\\=-1+i\\\\\text{It is in a form of a +bi so,}~ a = -1~ \text{and}~ b = 1[/tex]

In solving the following system of equations, what would you multiply by in order to eliminate the y?

Equation 1: x + y = 7 Equation 2: 5x + 2y = 8

A. 0
B. -5
C. -2
D. 2
E. 5

Give the solution to the system above

A. (7, 0)
B. (1, 6)
C. ( 8, - 1)
D. ( 3, 4)
E. ( -2, 9)

Answers

Answer:

D

E

Step-by-step explanation:

we need to multiply x+y=7 by   2

2x+2y=14

5x+2y=8

subtract

-3x=6

x=6/(-3)=-2

-2+y=7

y=7+2=9

solution is (-2,9)

what is the perimeter of a rectangular whose area is 92 square mm and length is 11.5 mm​

Answers

We are given

Area of rectangular is = 92 square mmLength of rectangular is = 11.5 mm

We are asked to find out the value of perimeter of the rectangular! Let's find it's breadth first!

We know that–

[tex]\qquad[/tex][tex] \purple{\bf\longrightarrow Area_{(Rectangular)} = Length \times Breadth} [/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow 92 = 11.5 \times Breadth [/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow Breadth = \cancel{\dfrac{92}{11.5}}[/tex]

[tex]\qquad[/tex][tex] \purple{\bf \longrightarrow Breadth = 8 \: mm}[/tex]

Now, Perimeter of rectangular –

[tex]\qquad[/tex][tex] \pink{\bf \longrightarrow Perimeter _{(Rectangular) } = 2( Length + Breadth) }[/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow Perimeter _{(Rectangular) }= 2( 11.5 +8) [/tex]

[tex]\qquad[/tex][tex] \sf \longrightarrow Perimeter _{(Rectangular) } = 2 \times 19.5[/tex]

[tex]\qquad[/tex][tex]\pink{ \bf \longrightarrow Perimeter _{(Rectangular) } = 39\: mm}[/tex]

Henceforth, Perimeter of rectangular is 39mm.

_______________________________________

Answer:

Perimeter = 39 mm

Step-by-step explanation:

In this question we are given with ,

Area of rectangle = 92 sq mm

Length of rectangle = 11.5 mm

And we're asked to find the perimeter of rectangle .

Solution : -

We know that ,

[tex] \pink{ \boxed{\sf{Area \: of \: rectangle = L × W}}}[/tex]

Where ,

L = length of rectangle

W = width of rectangle

So from this formula we can find the width of rectangle and equating it with 92 ( because 92 is the given area ) . Substituting value of length :

[tex] \longmapsto \: 11.5 \times W = 92[/tex]

Step 1 : Multiplying 11.5 and W :

[tex] \longmapsto \: 11.5W = 92[/tex]

Step 2 : Dividing by 11.5 on both side :

[tex] \longmapsto \: \frac{ \cancel{11.5}W}{ \cancel{ 11.5}} = \frac{92}{11.5} [/tex]

On further calculations we get :

[tex] \longmapsto \: W = \cancel{\frac{920}{115} }[/tex]

Step 3 : By cancelling 920 by 115 we get :

[tex] \longmapsto \: \purple{\boxed{ \bold{W = 8 \: mm}}}[/tex]

Therefore , width of rectangle is 8 mm .

Finding Perimeter :

We know that ,

[tex] \blue{ \boxed{ \sf{Perimeter \: of \: rectangle = 2 ( L +W )}}}[/tex]

Where ,

L = Length of rectangle

W = Width of rectangle

Substituting values in formula :

[tex] \longrightarrow \: 2(11.5 + 8)[/tex]

Step 1 : Solving parenthesis :

[tex] \longrightarrow \: 2(19.5)[/tex]

Step 2 : Multiplying 2 with 19.5 :

[tex] \longrightarrow \: \green{\boxed{ \bold{39 \: mm}}}[/tex]

Therefore, perimeter of rectangle is 39 mm.

#Keep Learning

Please help me with equation and more points for you if you can help me with how to approach these types of questions in the future, thanks!

Consider the following formula:

T = 4S – 1

Which of the following statements is true for this formula?

A. If S is greater than 0.5, T is positive.
B. If S is less than 1, T is negative.
C. If S is less than -0.25, T is positive.
D. If S is less than 0.25, T is positive.

Answers

A. If S is greater than 0.5, T is positive.

The others are false

Dan takes an airplane to visit his parents. He pays the airline a total of $450. The cost of the ticket is $315. The airline also charges $15for every pound that the luggage goes over the 50 pound is Dan's luggage over the 50 pound limit?

Answers

Answer:

9

Step-by-step explanation:

Start with the total amount Dan paid and subtract the part of the payment that is for the ticket.

450-315=135

Assuming that all of that $135 was for luggage fees and each pound over the limit costs $15, then the question is, how many times did Dan pay $15 until he'd paid the full $135 luggage fee.

So divide $135 by $15.

135/15=9

So his luggage weighted 59 pounds, which is 9 pounds over the limit.

Suppose ΔDEF has an exterior angle at vertex D. The measure of the exterior angle is (8x−2)º, m∠E=(3x−8)°, and m∠F=(4x+13)°. What is the measure of the exterior angle at vertex D?
A. 7°
B. 13°
C. 41°
D. 54°

Answers

The measure of the exterior angle at vertex D is: D. 54°

Recall:

The exterior angle theorem of a triangle states that the measure of an exterior angle equals the sum of the measures of two opposite interior angles of the triangle.

Thus:

In ΔDEF, (8x−2)º is an exterior angle at vertex D.

m∠E = (3x−8)° (interior angle)

m∠F = (4x+13)° (interior angle)

Therefore:

(8x−2)º = (3x−8)° + (4x+13)°

Solve for x

8x - 2 = 3x - 8 + 4x + 13

Combine like terms

8x - 2 = 7x + 5

8x - 7x = 2 + 5

x = 7

Exterior angle at vertex D = (8x−2)º

Plug in the value of x

= 8(7) - 2

= 54º (option D)

Learn more about exterior angle theorem on:

https://brainly.com/question/24756010

10 miles per hour is an example of an objects what?

Answers

I think the answer is speed

Step-by-step explanation:

Speed is the correct answer

Find the equation that represents the proportional relationship in this graph, for y in terms of x.

Answers

Answer:

y = 0.4 x

Step-by-step explanation:

I am an odd number. Take away one letter and I become even. What number am I?

Answers

Answer:

seven

Step-by-step explanation:

Lol thxx for the points

Pls give brainliest! Also, plz sub to kgirl633 on yt.

If 3 paintings cost $30, then how much does 1 painting cost?

Answers

Answer:

10$

Step-by-step explanation:

because 10$ + 10$ + 10$ equals 30$ so one is 30$

A furniture maker used 2/3 of a can of paint to paint some chairs. He used 1/6 of a can of paint for each chair. How many chairs did he paint?

Answers

Answer:

4 chairs

Step-by-step explanation:

Start with 2/3 can of paint: (2/3)

He used 1/6 of the can to paint each chair: (divided by 1/6)

Now use the 'keep, change, flip' method to get the expression: (2/3x6/1)

Then simplify your answer: (12/3)

Lastly simplify again: (4)

Thus, he painted 4 chairs.

Help pls, will give brainliest

Simplify 2^3 x 2^18

Answers

Answer:

it is 2^21

Step-by-step explanation:

Answer:

2^21

Step-by-step explanation:

add 3 and 18 together

dont change 2

It cost Faith $9.10 to send 91 text messages. How many text messages did she send if she spent $17.60?

Answers

Answer:

176

Step-by-step explanation:

9.10 / 91 = 1/10

17.60 x 1/10 = 176

Ms. jones is 50bls over weight. she decided to follow a diet to lose 50% of her excess weight by the first month, 20% by the end of second month and 25% more by the end of third month. how much of excess weight does she still has by the end of the third month

Answers

Answer:

5%

Step-by-step explanation:

You sum the lost excess weight: 50% + 20% + 25% = 95%. Meaning that she lost 95% of the excess weight. It remained just 5% to lose.

The data table represents the distance between a well-known lighthouse and a cruise ship over time. The cruise ship is travelling at uniform speed. Which equation represents the distance (y) from the lighthouse, based on the number of hours (x)? Number of Hours Distance from Lighthouse (in oceanic miles) 2 53 4 95.5 6 138 8 180.5 10 223 12 265.5 14 308 16 350.5 A. y = 42.5x + 10.5 B. y = 10.5x + 32 C. y = 21.25x + 10.5 D. y = 12.25x + 28.5 E. y = 12.5x + 10.5

Answers

Answer:

ddd

Step-by-step explanation:

250 + 200h = 300 + 180h
250 + 200h = 300 + 180h
− 180h − 180h
250 + 20h = 300

Answers

Answer:

  h = 2.5

Step-by-step explanation:

Continue the solution by subtracting 250 from both sides.

  250 -250 +20h = 300 -250

  20h = 50

Divide both sides by 20

  20h/20 = 50/20

  h = 5/2 = 2.5

Which graph best represents the equation x2 + (y – 1)2 = 3?

Answers

Answer:

Step-by-step explanation:

assuming the equation is x^2 + (y - 1)^2 = 3

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