Find the exact value of sin2Θ if tanΘ=[tex]\frac{-2\sqrt{5} }{5}[/tex] and 90 < Θ < 180.

Answers

Answer 1

Answer:

[tex]sin 2 \theta = \frac{4 \sqrt5}{9}[/tex]

Step-by-step explanation:

Identities used :

[tex]1. sin^2 \theta = 1 - cos^2\theta\\\\2. tan^2 \theta + 1 = sec^2 \theta\\\\3.cos \theta = \frac{1}{sec \theta} \\\\4. sin 2 \theta = 2 sin\theta cos\theta[/tex]

[tex]Given \ tan \theta = -\frac{2 \sqrt5}{5}\\[/tex]

[tex]we \ know \ tan ^2 \theta + 1 = sec^2\theta[/tex]

            [tex](-\frac{2 \sqrt 5}{5})^2 + 1 = sec^2 \theta\\\\\frac{4 \times 5}{25 } + 1 = sec^2 \theta \\\\\frac{20 + 25}{ 25} = sec^2 \theta \\\\\frac{45}{25} = sec^2 \theta \\\\sec \theta = \sqrt{ \frac{45}{25}}\\\\sec \theta = \sqrt{ \frac{9 \times 5}{5 \times 5}} \\\\sec \theta = \frac{3 \sqrt {5}}{5}\\\\[/tex]

[tex]We \ know \ cos \theta = \frac{1}{ sec \theta}[/tex]

[tex]So , \cos \theta = \frac{5}{3 \sqrt5}[/tex]

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

                 [tex]= 1 - (\frac{5}{3 \sqrt5})^2\\\\=1 - \frac{25}{9 \times 5}\\\\=1 - \frac{25}{45}\\\\=\frac{45 - 25}{45}\\\\=\frac{20}{45}\\\\=\frac{4}{9}[/tex]

    [tex]sin \theta = \sqrt{ \frac{4}{9}} = \frac{2}{3}[/tex]

[tex]Find \ sin 2 \theta[/tex]

[tex]sin 2 \theta = 2 (sin \theta \times cos \theta)[/tex]

        [tex]= 2 \times \frac{2}{3} \times \frac{5}{3\sqrt5}\\\\= \frac{4 \times \sqrt5 \times \sqrt5}{9 \times \sqrt 5}\\\\=\frac{4 \sqrt5}{9}[/tex]


Related Questions

0.202 round to the hundredth

Answers

Answer:

0.20

Step-by-step explanation:

Stuck on this one. I can’t remember the process to get the answer

Answers

the answer is 50 or D

a bookcase is 500mm wide how many of these bookcase will fill a
space 2m wide​

Answers

I think 4 but I could be wrong

A company has designed its new packaging for products to be shaped liked the prism shown. If the cost of packaging is $0.03 per square inch, find the total cost of the package shown. (10 inches horizontally, 4 inches vertically, and 4 inches on the side)

Answers

Answer:

$5.76

Step-by-step explanation:

We solve using the formula of the area of a rectangular prism

A = 2(LW + LH + WH)

The dimensions of the package are given as: 10 inches horizontally, 4 inches vertically, and 4 inches on the side

=2 × (4 × 10 + 4 × 10 + 4 ×4)

=192 square inches

If the cost of packaging is $0.03 per square inch, the total cost of the package is calculated as:

1 square inch = $0.03

192 square inches = x

Cross Multiply

= 192 × $0.03

= $5.76

Y’all know the answer?

Answers

9514 1404 393

Answer:

  (b)  36 in²

Step-by-step explanation:

The right triangle at lower right has a vertical leg of 3 and a hypotenuse of 5. Then the horizontal leg is ...

  √(5² -3²) = √16 = 4

Then the horizontal diagonal is 4+4 = 8. The vertical diagonal is 6+3 = 9. The area is half the product of the diagonals, so is ...

  A = 1/2(d1)(d2) = 1/2(8 in)(9 in) = 36 in²

__

You could figure the areas of the triangles separately, but you would come to the same result. This formula is good for a rhombus or a kite (or a square, which is also a rhombus), because the diagonals are perpendicular to each other.

A bank account starts with $3.00. The amount in the account doubles every year .

Answers

Answer:

Step-by-step explana

multiply it by 2 or sdd itself to it

The  account will have $1536.007 after 9 years.

Part A:

To express the total amount of money A(t) in the account after 7 years, we can use the formula:

A(t) = P[tex](2^t)[/tex]

where:

A(t) is the total amount in the account after t years,

P is the initial amount in the account (starting with $3.00 in this case),

t is the number of years.

Substituting the values into the formula, we get:

A(t) = 3 ([tex]2^7[/tex])

A(t) = 3 x 128

A(t) = 384

Therefore, the total amount of money in the account after 7 years is $384.

B) To find out after how many years the account will have $1536.007, we need to solve the equation:

1536.007 = 3 [tex](2^t)[/tex]

Dividing both sides of the equation by 3, we get:

512.0023333333 = [tex]2^t[/tex]

Taking the logarithm (base 2) of both sides, we have:

log2(512.0023333333) = t

t = 9.000317.

Therefore, the account will have $1536.007 after 9 years.

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if a/4=2/3, then (a-4)/4 would equal
a. -2/3
b. -1/3
c. 0
d. 1/3

Answers

Answer:

b. -1/3

Step-by-step explanation:

a/4=2/3

a=8/3

(a-4)/4

(8-12)/12

=-4/12

=-1/3

Answer:

-1/3

Step-by-step explanation:

a/4=2/3

Multiply each side by 4

a/4 *4=2/3 *4

a = 8/3

(a-4)/4

(8/3 - 4) /4

Getting a common denominator

(8/4 - 12/3) /4

(-4/3)/4

-1/3

can you help me find the code



link/picture in the comments

Answers

Answer:

????? sus

Step-by-step explanation:

sussy baka????

among sus

Sgdndgdbdbxvddns did she she she she didn’t yyyyyyyyyyy

A teacher is buying supplies for two art classes. For class 1, the teacher buys 24 tubes of paint, 12 brushes, and 17 canvasses. For class 2, the teacher buys 20 tubes of paint, 14 brushes, and 15 canvasses. Each tube of paint costs $3.35, each brush costs $1.75, and each canvas costs $4.50. Compute the following matrix multiplication to determine how much the teacher spent on each class.

Answers

Class 1 =$177.90
Class 2 =$159


Class 1

24 tube of paint / $3.35 each
12 brushes/ $1.75 each
17 canvases/$4.50 each
Total cost of paint= $80.40
Total cost of brushes=$21
Total cost of canvases= $76.50
Total spent on class 1 = $177.90

Class 2

20 tubes of paint/$3.35 each
14 brushes/$1.75 each
15 canvases/ $4.50 each
Total cost of paint=$67
Total cost of brushes =$24.50
Total cost of canvases=$67.50
Total spent on class 2 = $159

could u help me last part :)

Answers

Answer: 288pi in cubed

Step-by-step explanation: because area of a circle is pir^2 so 36*8=288

Answer: 288pi in^3
Explanation:
Volume Formula= piR^2h (R= Radius and H= Height)
So pi*6^2*8 gets you 288pi ^3
Keep the formula in mind to help you with further problems.

Hope this helps you. If available please give me a branliest. It would be much appreciated!

- Mathhotdog •~•


How does the range of g(x)=6/x compare with the range of the parent function f(x)=1/x?

Answers

Answer:

The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all nonzero real numbers.

Step-by-step explanation:

The range of the function is the set of real number for [tex]y[/tex]. The rational function of the form [tex]y = \frac{a}{x}[/tex], where [tex]a[/tex] is a constant, has a range represented by the subset of nonzero real numbers. This is: [tex]Ran\{f(x)\} = \mathbb{R}-\{0\}[/tex]

Hence, the correct answer is: The range of both [tex]f(x)[/tex] and [tex]g(x)[/tex] is all nonzero real numbers.

which pairs of angles in the figure below are vertical angles select all that apply

Answers

Answer:the left one

Step-by-step explanation:

Approximately how long will it take $200 to double to $400 when the annual interest rate is 8 1/2?

Answers

Answer:

200/17 years

Step-by-step explanation:

Simple interest = (principle * time * rate) / 100i

Please help. I am very confused about this problem.

Answers

jzgsgßiqhwgwgah I don't know

Answers:

number of sides = 15regular polygon name = regular 15-gon

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

Explanation:

If 156 degrees is the interior angle measure, then 180-156 = 24 is the exterior angle measure.

Divide 360 over this to find that 360/24 = 15

This means the regular polygon has 15 sides.

I'm using the idea that if n is the number of sides, then 360/n is the exterior angle measure. So 180 - (360/n) is the interior measure.

Which is the degree measure of an angle whose tangent is 1.19? Round the answer to the nearest whole number. A. 48° B. –48° C. 50° D. –50°

Answers

9514 1404 393

Answer:

  C.  50°

Step-by-step explanation:

The angle whose tangent is 1.19 is ...

  arctan(1.19) ≈ 49.9585° ≈ 50°

The 50° measure of an angle whose tangent is 1.19.

What is tangent?

Tangent in geometry,  is defined as "a line or plane that touches a curve or curved surface exactly at one point" .

According to the question,

The degree measure of an angle whose tangent in 1.19.

In order to an angle only if arctan(119) = 49.9585 ≈ 50.

Hence, the 50° measure of an angle whose tangent is 1.19.

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Enter the value of x so that the expression (1.8a−5.7)+(xa+3.2) is equivalent to −1.6a+2.5.

Answers

Answer:

Step-by-step explanation:

ax+1.8a−2.5

i’m horrible at math, can anyone help?

Answers

Answer: no I'm actually horrible at math too sorry

Which polynomial below could produce this graph?

Answers

Answer:

f(x) = (x + 20)(x - 24)(x + 10)(x + 12)

Step-by-step explanation:

This is an equation of degree 4 and as the beginning of the graph descends from negative x the polynomial will have a positive leading coefficient. The graph is roughly W shaped.

It also has zeroes at x = -20,-12 ,-10 and x = 24.

So it is the first option.

Find the volume of a regular square pyramid with base edge 10 ft. and height 12 ft.
120 ft
75ft?
400 ft
D 300 ft?

Answers

Answer:

V = 400 ft^3

Step-by-step explanation:

The area of the base of this regular square pyramid is (10 ft)^2, or 100 ft^2.

Recalling that the area of a pyramid is V = (1/3)(base area)(height), in this case we get V = (1/3)(100 ft^2)(12 ft)  =  400 ft^3

Holly cuts 2 ribbons into tenths for a craft project how many 1/10 size ribbons does she have

Answers

Answer:

Holly would have 20 1/10 sized ribbons.

Step-by-step explanation:

One whole ribbon would equal out to 10, this number multiplied by 2 would be 20. Therefore meaning she should have 20 1/10 sized pieces of ribbon.

Solve for x in the equation

Answers

Answer:

its the first one

Step-by-step explanation:

2,-6 or -6,2 , so its a .

find (a) the perimeter and (b) the area of the figure. use 3.13 or 22/7 for n. round your answer to the nearest hundredth, if necessary

Answers

Answer:

;)))

Step-by-step explanation:

Which equation represents a line which is perpendicular to the line 6x+y=-4

Answers

Answer:

y = 1/6x - 4

Step-by-step explanation:

y = -6x - 4  

current slope is -6 so the slope of a line perpendicular would be 1/6

y = 1/6x - 4


Part A: Estindlate the solution from the graph. -
Part B: What is the equation of each line in the system? blue line: _ and red line:

Answers

Answer:

Part A

The estimated solution of the graph is (37/29, -30/29)

Part B

The equation of the blue line is y = 0.6·x - 1.8

The equation of the red line is y = (-4/3)·x + 2/3

Step-by-step explanation:

Part A

From the given graph, we have two lines, one red and one blue line, intersecting in Quadrant IV

Given that the equation of the lines are also required, we find the solution of the graph, through the equation of the lines as follows;

The points through which the blue line passes are (-2, -3), and (3, 0)

The slope of the blue line, [tex]m_b[/tex] = (0 - (-3))/(3 - (-2)) = 0.6

Therefore, we have;

y - 0 = 0.6·(x - 3)

∴ The equation of the blue line is y = 0.6·x - 1.8

The approximate points through which the red line passes are (-1, 2) and (-2.5, 4)

The slope of the red line, [tex]m_r[/tex] = (4 - 2)/((-2.5) - (-1)) = -4/3

Therefore, we have;

y - 2 = (-4/3)·(x - (-1)) = (-4/3)·x - 4/3

∴ The equation of the red line is y = (-4/3)·x - 4/3 + 2 = (-4/3)·x + 2/3

y = (-4/3)·x + 2/3

The solution for the graph is the point where the y-values are equal

Therefore, wat the solution point, y = y, and 0.6·x - 1.8 = (-4/3)·x + 2/3

0.6·x + 4/3·x  = 1.8 + 2/3

x = (1.8 + 2/3)/(0.6 + (4/3)) = 37/29 ≈ 1.28

At the solution of the graph, y = 0.6 × (37/29) - 1.8 = -30/29

Therefore, the estimated solution of the graph is (37/29, -30/29)

Part B

From the above solution of the graph, we have;

The equation of the blue line: y = 0.6·x - 1.8

The equation of the red line: y = (-4/3)·x + 2/3

The bars of a histogram should be shown in increasing order. true or false

Answers

Answer:

false it can be in any order but must be according to the set of data

WILL GIVE BRANLIEST!!! pls help tysm!!!

Answers

Try this I could have misunderstood the question but this it’s what I got don’t mind the hand writing

Please help fast!! What is the range of the scores shown in the stem and leaf plot
95
40
58
37

Answers

Answer:

37

Step-by-step explanation:

Highest take the lowest

95-58=37

Malik wanted to give away \frac{1}{5} 5 1 ​ of his bag of balloons to his 3 friends. What fraction of balloons will he give away?

Answers

Answer:

The answer is 3/5

Step-by-step explanation:

The amount of balloon to be given away= 1/5

The number of friends to

receive the balloon = 3

Therefore the total fraction of balloons that he gave away = 1/5 × 3

=3/5

what is the equation, in point-slope form, of the ljne that is perpendicular to the given line and passes through the point (-4,-3)? ​

Answers

Answer:y+3=1/4(x+4)

Step-by-step explanation:

First find the slope of the line with the points -1,1 and 0,-3

1-(-3)/-1-0 = -4

perpendicular is negative reciprocal which is 1/4

now we have the slope, and a point so we can put it in point slope form

y+3=1/4(x+4)

point slope form is y-y1 = m(x-x1)

with x1,y1 being the point and m being the slope

SOMEONE PLEASE HELP THIS IS DUE TOMROROW EZ WORK


PLEASE ANSWER THEM PROPERY FULL SENTENCES

Answers

Answer:

1.) At times, designing a good structure with a specific function may often be difficult. If the structure is not well-designed or strong enough for the function it will not properly work. So in order for the design to be well-built, both the structure and function must cooperate.

2.) Symmetry is a balanced arrangement on the opposite sides of a structure. In order for for a structure to be stable and properly work without complications, it most commonly needs to be symmetrical. This is a very important part of designing a structure.

3.) If the structure cannot withstand the function nor the possible forces that it may encounter. It is likely that it will break or even be completely destroyed.

4.) Shape, line, color, texture, movement, space. The designer may have taken into consideration whom the desk may be used by for the shape and space. Color, texture, and line may have been based on the environment (ex. A carpenter, student, computer desk) it would be in. Although the designer may not have an exact knowledge of where the desk would be, he still could consider what the desk could "possibly" be used for. Once again, the designer could take into consideration the user, for the movement of the desk. If the desk was to be moved around on wheels, or possibly could even fold. The designer must take into consideration EVERY detail.

6.) When people design something, often times you do not know how well that design is going to work without testing it with a prototype. Yes, prototypes are expensive. Yet, if they were to build something without testing their design, something may be wrong with it. So as a result, you will spend more money manufacturing something with a defect than testing it with a prototype.

For question 5, I think it might be best if you answer that one. It is based on YOUR opinion and what YOU use. If you are asked about it, they will know it's from you and your opinion. Lol! But I hope I helped you out with the other questions! ;)

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