Using half angle identities, find an EXACT expression for sin(7π/12).

Answers

Answer 1

Answer:

±[tex]\frac{1+\sqrt{3} }{2\sqrt{2} }[/tex]

Step-by-step explanation:

We can rewrite [tex]sin(\frac{7\pi }{12} )[/tex] as [tex]sin(\frac{7\pi }{6} (\frac{1}{2} ))[/tex]. The half-angle identity for sin tells us that [tex]sin(\frac{x}{2} ) = \sqrt{\frac{1 - cos(x)}{2} }[/tex] (plus or minus). Now, we can plug in [tex]\frac{7\pi }{6}[/tex] for x. When we do that, we get [tex]\sqrt{\frac{1 - (-\frac{\sqrt{3}}{2}) }{2} }[/tex] =  ± [tex]\frac{1+\sqrt{3} }{2\sqrt{2} }[/tex].

Hope this helped! :)


Related Questions


I NEED HELP WITH THIS QUESTION PLEASE, i don't have much time T^T

i'll give brainliest and points, thank you in advancee <33

an explanation for future reference would be appreciated!!^^​

Answers

Answer:

Option b is the correct answer

Step-by-step explanation:

[tex]\cos x = -\frac{12}{13}[/tex] (Given)

Formula relating sin x and cos x is given as below:

[tex]\sin^2x = 1-\cos^2x[/tex]

[tex]\implies \sin^2x = 1-\bigg(-\frac{12}{13}\bigg)^2[/tex]

[tex]\implies \sin^2x = 1-\frac{144}{169}[/tex]

[tex]\implies \sin^2x = \frac{169-144}{169}[/tex]

[tex]\implies \sin^2x = \frac{25}{169}[/tex]

[tex]\implies \sin x =\pm\sqrt{ \frac{25}{169}}[/tex]

[tex]\implies \sin x =\pm \frac{5}{13}[/tex]

It is given that: 180° < x < 270°. This means x falls in the third quadrant. In third quadrant sin ratio is negative.

[tex]\implies \sin x =- \frac{5}{13}[/tex]

Now, we will find the value of tanx by dividing sinx by cosx.

[tex]\implies \tan x =\frac{\sin x}{\cos x}[/tex]

[tex]\implies \tan x = \frac{-5/13}{-12/13}[/tex]

[tex]\implies\red{\bold{ \tan x =\frac{5}{12}}}[/tex]

tan (90° + x) and tan x both lie in the interval 180° < x < 270°. So, the values of both will be equal.

[tex]\implies \tan (90\degree + x ) =\tan x[/tex]

[tex]\implies \huge{\purple{\tan (90\degree + x ) =\frac{5}{12}}}[/tex]

A Block of wood has a mass volume of 0.8g and volume of 16.0cm³. what is the density?

Answers

Answer:

[tex]0.05cm {}^{3} [/tex]

Step-by-step explanation:

[tex]density \: is \: the \: mass \: per \: unit \: volume \: of \: an \: object \: \\ density = \frac{m}{v} \\ density = \frac{0.8}{16} = 0.05cm {}^{3} [/tex]

Tyrone receives a discount of $8.40 on a hat that normally costs $28.00 .
what percent discount did he receive on the hat
explain how you know
please explain for me

Answers

Answer:

30%

Step-by-step explanation:

percentage = (discount/total amount)*100

= (8.40/28)*100=30%

5. Find ​(f◦​g)(x) and ​(g◦​f)(x) and the domain of each.

​f(x)=x2−3​, ​g(x)=2x−

Answers

Answers:

[tex](f \circ g)\;(x) = 4x^2 - 12x + 6\\\\(g \circ f)\;(x) = 2x^2-9\\\\[/tex]

The domain for both is "all real numbers".

============================================================

Explanation:

The work is shown below in the attached image.

The domain for each composite function is the set of all real numbers because we don't have to worry about things like dividing by zero, or taking the square root of a negative number. Any x value is allowed.

A. -4
B. 0
C. 1
D. 4

Answers

Answer: B) 0

Explanation:

[tex]\rightarrow \sf y = \dfrac{1}{2} x - 2[/tex]

insert x = 4

[tex]\rightarrow \sf y = \dfrac{1}{2} (4) - 2[/tex]

simplify

[tex]\rightarrow \sf y = 2 - 2[/tex]

subtract

[tex]\rightarrow \sf y = 0[/tex]

The first TV Chrystal had was 7 inches by 9 inches. She now has a TV that is 56 inches by 72 inches. What is the scale factor?

Answers

Answer:

8

Step-by-step explanation

to find the scale factor you find out by how many times the numbers have gone bigger or smaller

7inches by 9inches

56inches by 72inches

7×8= 56

9×8=72

7 and 9 have changed 8 times more so the scale factor is 8

solve for x
x/7 = 3/5 enter answer as decimal ​

Answers

Hey there!



ORIGINAL EQUATION:
x/7 = 3/5

CROSS MULTIPLY THE FRACTIONS

x(5) = 3(7)

5(x) = 3(7)

SIMPLIFY IT!

5x = 21

DIVIDE 5 to BOTH SIDES

5x/5 = 21/5

SIMPLIFY IT!
x = 21/5

x = 4 1/5


Therefore, the answer should be:

x = 21/5

OR

x = 4 1/5


EITHER OF THOSE SHOULD WORK BECAUSE THEY ARE BOTH EQUIVALENT TO EACH OTHER!


Good luck on your assignment & enjoy your day!



~Amphitrite1040:)

The stem-and-leaf plot shows test scores for students in Math 7. How many students earned more than a 65 on their test? Key 4|5 = 45 A) 58 students B) 28 students C) 60 students D) 65 students

Answers

the answer is b

Step-by-step explanation:

hope this helps if not let me know have a blessed day

I need help with this problem

Answers

Answer:

a = -4

Step-by-step explanation:

(a + 2)/2 = - 1

a+2 = -1 * 2

a = - 2 - 2

a = -4

Answer:

-2.5

Step-by-step explanation:

soo your objective is to make a alone

first remove the denominator

a+2 / 2 = -1

a + 2 = -1/2

now minus 2 to  both sides

a = -1/2 - 2

a = -2 1/2

Solve the equation X = 64 for x.
ОА. -32, 32
O B. -8, 8
OC. 8
OD 32

please help​

Answers

Answer:

B

Step-by-step explanation:

Answer:

the answer is b

Step-by-step explanation:

the path of a cliff diver as he dives into a lake, is given by the equation y = -(x-10)^2+75, where y metres is the diver’s height above the water and, x meters is the horizontal distance travelled by the diver. what is the maximum height the diver is above the water?

Answers

Answer:

The highest point will be (10, 75)

Step-by-step explanation:

Help plss. Worth 20 points<3

What do animals that are carnivores eat?

fish and insects
other animals
plants and fungus
whatever they can find

Answers

Answer:  Other animals

Step-by-step explanation:

1000 ft.
Problem 3.2
100 ft.
A large rectangular swimming pool is 1000 feet long,
100 feet wide, and 10 feet deep.
The pool is filled to the top with water.
How much water does the pool hold?
Submit

Answers

Answer:

1,000,000

Step-by-step explanation:

you just get the Volume of the shape

HELP NOW PLEASEE
h(x)=x^(2)+x+9

find h (-2)
find h (4)
and find h (0)

Answers

Answer:

11, 29, 9

Step-by-step explanation:

substitute x = - 2, 4, 0 into h(x)

h(- 2) = (- 2)² + (- 2) + 9 = 4 - 2 + 9 = 2 + 9 = 11

h(4) = 4² + 4 + 9 = 16 + 4 + 9 = 29

h(0) = 0² + 0 + 9 = 0 + 0 + 9 = 9

The right rectangular prisms are similar. which statements are correct? check all that apply. the angles in the smaller prism measure 90 degrees. the perimeter of the rectangular bases changes by a factor of 2. the surface area changes by a factor of 8. the larger prism has twice the volume of the smaller prism. the area of the rectangular bases changes by a factor of 4.

Answers

The true statement about the right rectangular prisms include:

The angles in the smaller prism measure 90 degrees.The perimeter of the rectangular bases changes by a factor of 2.The rectangular bases changes by a factor of 4.

How to illustrate the prism?

It should be noted that a prism simply means a shape that has two identical shapes that face each other.

Here, the angles in the smaller prism measure 90 degrees and the perimeter of the rectangular bases changes by a factor of 2.

Learn more about prism on:

brainly.com/question/23963432

#SPJ4

Tom has 20 girls in his seventh-grade class. The ratio of girls to boys is 5:4. How many boys does he have in his seventh-grade class?

Answers

Answer:

16 boys

Step-by-step explanation:

in ratio form girls are represented by 5 so if 5 equals to 20 what about 4 and that's how I got the answer good day.

Agree & disagree statements: CIrcles

Circle A has a diameter of 18 inches.
Circle B has a circumference of 36 inches.

write the letter of the card in the correct column next to the letter, write your explanation as to why it belongs in the agree or disagree columns.

1. Circle A has an approximate circumference of 56.5 inches. true or false? explain.
2. Circle A has an area of 324r in2, True or false? explain
3. Circle A is approximately 151 square inches greater than Circle b. True or false ? explain.

Answers

Answer:

Hope the pictures will help you

Express 0.57 in the form p where p and q are integers o and q # 0

please give with correct step everyone ​

Answers

Answer:

57/100

Step-by-step explanation: 0.57 can also be written as 57/100 which is equal to 0.57

a right triangle has a hypotenuse of 25 inches and a height of 7 inches .what is the area of the triangle?

Answers

87.5

25x7=175

175/2=87.5

What is the greatest common factor of the numerator of ?

Answers

The greatest common factor of the numerator and denominator of the rational expression is x - 4

How to determine the greatest common factor?

The fraction expression is given as:

[tex]\frac{5x-20}{x^2-2x-8}[/tex]

Factorize the numerator and the denominator

[tex]\frac{5x-20}{x^2-2x-8} = \frac{5(x-4)}{(x- 4)(x + 2)}[/tex]

Cancel out the common factor

[tex]\frac{5x-20}{x^2-2x-8} = \frac{5}{(x + 2)}[/tex]

The common factor that was canceled out is x - 4

Hence, the greatest common factor of the numerator and denominator of the rational expression is x - 4

Read more about greatest common factors at:

https://brainly.com/question/10076354

#SPJ1

which equation represents a line which is parallel to the line y=8/7x-6?

Answers

Answer: 8x-7y = 56

Step-by-step explanation:

complete the solution of the equation. find the value of y when x equals -2. -9x-3y=6

Answers

Answer:

y= 4

Step-by-step explanation:

-9x-3y=6

Let x = -2

Substitute for x in the equation

-9(-2) -3y = 6

18 -3y = 6

Subtract 18 from each side

18-3y-18 = 6-18

-3y = -12

Divide by -3

-3y/-3 = -12/-3

y = 4

please answer!!!! will mark brainliest!!!

Answers

Answer:

6.42 %

Step-by-step explanation:

Formula    FV = PV ( 1 + i)^n        i = periodic interest in decimal

                                                 FV = future value    PV = present value

                                                    n = periods ( years in this case)

3412.23 = 2500 ( 1 + i)^5

3412.23/2500  = (1+i)^5

1.364892 = (1+i)^5

1.0641 = 1+ i

i = .0642      or    6.42 %

Does anyone knows the answers to these

Answers

Median is 17
Range is 17.4
IQR is 6

Can someone please answer this, ill give you brainliest Would be very appreciated.

Answers

Answer:

See below ~

Step-by-step explanation:

More revenue would be generated at $5 than $17 because on the graph, when the price is at $5, there is about $3750 in revenue compared to when the price is $17, the revenue is $2500.The company should sell their product at $10. At this price, the revenue they will make is $5,000.The domain is the possible intervals in which x lies. Therefore, the domain is : 0 ≤ p ≤ 20.

REALLY REALLY NEED HELP!!!! MATH GENIUSES OUT THERE!!!! ANYONE!!!!!! FOR EDGE!!!!!!

Answers

Answer:

on the attached pdf

Step-by-step explanation:

GIVING BRAINLIEST!!!!!

Answers

Answer:

x = 18

Step-by-step explanation:

The angles (x)° and (4x)° are complementary, meaning they form a 90° angle.

x + 4x = 90

Combine like terms :

x (1 + 4) = 905x = 90

Divide both sides by 5 :

5x/5 = 90/5x = 18

What is the area,in square meters,of the isosceles trapezoid?

Answers

Step-by-step explanation:

the area of a trapezoid is

(base1 + base2)/2 × h = (18.6 + 9.2)/2 × 7.2 =

= 27.8/2 × 7.2 = 13.9 × 7.2 =

= 100.08 m²

Please help

Use the following data set to answer questions 9-16:

11, 18, 8, 15, 24, 14 9.

9. Identify the median. Round to the nearest tenth.

10. Calculate the mean. Round to the nearest tenth.

11. Calculate the mode. Round to the nearest tenth.

12. Predict how the median will change if a 21 is added to the data set. Identify the new median.

13. Predict how the mean will change if an 18 is added to the data set. Calculate the new mean.​​

Answers

Answer:

9. Median: 14

10. Mean: 14.1

11. Mode: No Mode

12. New Median: 14.5

13. New Mean: 14.625

Simplify this expression.

8(h-4)-h-(h+7)

Solve step-by-step

Answers

Answer:

6h - 39 or 3(2h - 13)

Step-by-step explanation:

Distribute the terms in the parentheses.

8(h - 4) - h - (h + 7)8h - 32 - h - h - 7

Combine like terms

8h - h - h - 32 - 76h - 393(2h - 13) [by grouping]

8 (h - 4) - h - (h + 7)

8h - 32 - h - h - 7

6h - 39

3 (2h - 13)

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