Which set of steps can be used to prove the sine sum identity, sin(x y) = sin(x)cos(y) cos(x)sin(y)?

Answers

Answer 1

The trigonometry identity sin(x + y) = sinx cosy + cosx siny.

What is sin(x + y) identity in trigonometry?

sin(x + y) is one of the identities in trigonometry for compound angles.

The angle (x + y) represents the compound angles.

sin(x + y) = sinx cosy + cosx siny

To prove sin(x + y) = sinx cosy + cosx siny

Consider OX as a rotating line anti-clockwise. Let angle XOY = a

the making of an acute angle b the rotation in the same direction is

angleYOZ = b , angle XOZ = a + b

From triangle PTR,

∠TPR = 90 - ∠PRT , ∠ROX = a

From the right-angled triangle PQO

sin(a + b) = PQ/OP

= (PT + TQ) / OP

= PT/OP + TQ/OP

= PT/PR × PR/OP + RS/OR × OR/OP

= cos (∠TPR ) sinb + sina cosb

= sina cosb + cosa sinb

if we replace a=x and b=y

Therefore, sin(x + y) = sinx cosy + cosx siny.

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Which Set Of Steps Can Be Used To Prove The Sine Sum Identity, Sin(x Y) = Sin(x)cos(y) Cos(x)sin(y)?

Related Questions

PLS HELP ASAP FIRST CORRECT ANSWER GETS BRAINLEIST​

Answers

Answer:

b ≈ 18.3303

[tex]b = \sqrt{{c}^{2} - {a}^{2} } [/tex]

[tex]b = \sqrt{ {19}^{2} - {5}^{2} } [/tex]

[tex]b = 18.3303[/tex]

An integer is chosen at random from 1 to 50 inclusive. Find the probability that the chosen integer is divisible by 3. 8/25 3/10 3/50

Answers

How many numbers from 1 to 50 are multiples of 3?

3, 6, 9, 12, 15, 18 .......

Let's change the start and end value of the array and find the number of terms

Start at 3 and go all the way to 48 because those are the first and last multiples of 3 in this array.

There is a formula that allows us to quickly find the number of terms

We subtract the first term from the last term and divide by the amount of increase, then we add 1.

(48 - 3) / 3 + 1   =   16 numbers are exactly divisible by 3.

We have 50 numbers and 16 of them divisible by 3

16 / 50  = 8 / 25 probability

The probability that the chosen integer is divisible by 3 is 8/25 if an integer is chosen at random from 1 to 50 inclusive option first is correct.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

We have the number from 1 to 50.

Total numbers between 1 to 50 or total outcomes = 50

Total favorable outcomes = total number which is divisible by 3

[tex]=\frac{48-3}{3} +1[/tex]

= 15 + 1

= 16

Now probability will be:

= 16/50

= 8/25

Thus, the probability that the chosen integer is divisible by 3 is 8/25 if an integer is chosen at random from 1 to 50 inclusive option first is correct.

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A cube is sliced as shown. Find the area of the cross section formed by the slice.

Answers

Answer: 5√(50) = 35.36 m^2

Step-by-step explanation:

The cross section is a rectangle, so its area formula is: Area = length * width.

If you look, the width is the diagonal of the side of the cube; thus, you can use Pythagorean theorem to find its measurement: a^2 + b^2 = c^2 → 5^2 + 5^2 = c^2 →

50 = c^2 → c = √(50)

Now, use the area formula and get: Area = 5 * √(50) = 5√(50) = 35.36 m^2 :)

help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Febuary 10th because on the left colom it showss the dates just look for the 10

Jen bought a cinnamon bun for $3. 42 and a giant candy cane for $5. 76. She then used the rest of her money to buy a notebook. She spent a total of $12. 83. How much money did Jen spend on the notebook? (5 points)


$9. 41

$7. 07

$3. 65

$2. 34

Answers

Answer:

She spent $3.65 on the notebook

Step-by-step explanation:

5.76 + 3.42 = $9.18

12.83 - 9.18 = $3.65

its literally 15 points
How do i find lateral area?
dont answer in a confusing way please i just need to understand this :(

Answers

Answer:

There are many areas but

Step-by-step explanation:

Area of square is L × W

where you multiply both length × width you get the answers squared

Area of a cube is L × W × H

this is where you multiply all length × width × height and get the answer cube

please help? , no decimals please,please explain to see picture. ​

Answers

Answer:

[tex]8x\sqrt{3xy[/tex]

Step-by-step explanation:

6 cm
6cm
6 cm
5 cm
4 cm
8cm
Solid B
Solid A
Which of the above solids has the larger surface area?
O O A. Solid A
O
B. Solid B
C. They have the same surface area.

Answers

Answer:

Solid A

Step-by-step explanation:

Surface area of a cube: 6 x a², where a is the side.

= 6 x 6²

= 6 x 36

= 216 cm²

Surface area of the cuboid/rectangular prism: 2(lw + wh + lh), where l is the length, w is the width, h is height.

= 2((5 x 4) + (4 x 8) + (5 x 8))

= 2(20 + 32 + 40)

= 2(92)

= 184 cm²

Therefore, Solid A has the larger surface area compared to Solid B.

select all fo the expressions that are equivilent to 6x + 1 -(3x-1)

Answers

6x+1-(3x-1)

6x+1-3x+16x-3x+1+1

=3x+2

There are 221 students on a field trip.
. Five students ride in a van.
. The rest of the students fill 6 buses.
Enter an equation that can be solved to find the number of students, s, that are on each bus. Enter your response in
the first response box.
Enter the number of students that are on each bus. Enter your response in the second response box.

Answers

The equation that models the students is a linear equation

The equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36

How to determine the equation?

The given parameters are:

Students = 221

Van = 5

The rest students = 6 buses

Start by calculating the number of students remaining:

Remaining students = 221 - 5

Remaining students = 216

Represent the number of students in each bus with x.

So, we have:

6 buses * x  = Remaining students

This gives

6x = 216

Divide both sides by 6

x = 36

Hence, the equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36

Read more about linear equations at:

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Knowing that ΔBIG ≅ ΔFNS, an angle pair that is NOT necessarily congruent is:

Knowing that ΔDAL ≅ ΔEKS, a side pair that is NOT necessarily congruent is:

Answers

solutions:

1) G ≅ F

2) DA ≅  ES

Explanation:

Q)1

ΔBIG ≅ ΔFNS

pairs that are congruent:

B ≅ FI ≅ NG ≅ S

From the list given,

→ G ≅ F is not necessarily congruent.

Q)2

ΔDAL ≅ ΔEKS

pairs that are congruent:

DA ≅  EKAL ≅  KSDL ≅  ES

From the list given,

DA ≅  ES  is not necessarily congruent.

Usually the congruence is done according to naming

So

∆BIG≅∆FNS

<B=F

<I=<N

<G=<S

Option A

#2

Check the naming

∆DAL≅∆EKS

So

DA=EK

And DA may not be equal to ES

So option D

What is the domain of the following {(1,3),(2,7),(3,-1)

Answers

Answer: this is a function.

f(x)=y

Step-by-step explanation:

domain -> 1,2,3

values: 3,7,-1

-12 = -3y

How to Solve?

Answers

Answer:

y = 4

Step-by-step explanation:

Given:

[tex]-12=-3y[/tex]

Solve:

[tex]\mathrm{Divide\:both\:sides\:by\:}-3[/tex]

[tex]\frac{-3y}{-3}=\frac{-12}{-3}[/tex]

[tex]\mathrm{Simplify}[/tex]

Note: Negative + Negative = positive

y = 4

~lenvy~

Divide both sides by -3 and y = 4

each team in a youth soccer league pays $784 to join the league. if a team consists of 12 players and the fee is divided equally among the players, how much does each player pay?

Answers

Answer:

$65.33

Step-by-step explanation:

12x = 784

÷12     ÷12

x = 65.33

They would each have to pay $65.33.

I hope this helps!

a rectangular painting is 24 inches wide and 20 inches tall without the frame. With the frame, it is 28 inches wide and 24 inches tall. What is the area of the frame not covered by the painting?

Answers

Answer:

191

Step-by-step explanation:

do the frame with the pic first that is

28*24=672

next just the pic

24*20=480

next subtract the pic from the frame

672-480=191

Actually help PLSS
(will give brainliest)

Answers

Let's see point E in its original position: (3.-4)

Now lets transform the point (x,y) -->  (x + 8, y +5)

   

               (3, -4) --> (3 + 8, -4 + 5) --> (11, 1)

Therefore coordinate E's new position is (11, 1)

Hope that helps!

             

what is the slope of the line on the graph need answer ASAP please thank you I'm in k-12​

Answers

The answer is -1 your welcome

I have 936 pencil . A box holds a dozen pencil . How many boxes will I be able to fill​

Answers

Answer:

you will fill 78 boxes

Step-by-step explanation:

dozen = 12

936 divided by 12=78

explain how you know whether or not the point (0.75, 0.25) is on the unit circle.

Answers

Answer:

The point (0.75, 0.25) is not on the unit circle.

Step-by-step explanation:

The unit circle has radius 1, so:

[tex] {.75}^{2} + {.25}^{2} = .5625 + .0625 = .625 [/tex]

help me on both questions as attached below.
Also it's workings on how to get that if possible

Answers

Answer:

a) 160km

b) it will take 3.2 hours or 192 minutes or 3 hours and 12 minutes

Step-by-step explanation:

a) d=speedxtime

so, 64x2. 5=160km

b) time=d/s

so, 160/50

it will take 3.2 hours or 192 minutes or 3 hours and 12 minutes

Felipe is making triangles for a stained glass window, he made the design shown but wants to change it. Felipe wants to move the purple triangle to the corner. The purple piece has side lengths of 4.5 inches, 6 inches, and 7 inches. Can the purple piece be moved to the corner?

Answers

We have sides of triangle as [tex]4.5[/tex] inches, [tex]6[/tex] inches and [tex]7[/tex] inches.

So the sum of square of two smallest side is-

[tex]=4.5^2+6^2[/tex]

[tex]=20.25+36[/tex]

[tex]=56.25[/tex]

Now lets find the value of square of longest side of triangle-

[tex]=7^2[/tex]

[tex]=49[/tex]

Now from both value

[tex]49[/tex] [tex]\neq[/tex] [tex]56.25[/tex]

[tex]7^2[/tex] [tex]\neq[/tex] [tex]4.5^2+6^2[/tex]

So from Pythagoras theorem the given triangle is not a right triangle so it can not moved to the corner.

Thus, Since the triangle is not a right triangle therefore it can not moved to the corner.

What is the measure of <1?

Answers

Answer:

the measure of ∠1 is 92 degrees

Step-by-step explanation:

Can someone please answer the attachment​

Answers

Step-by-step explanation:

linear pair

linear pair

alternate angles.

alternate angles

cointerior angles

I will hope that you like my answer

Help me with this question on congruent triangles? 20 points

Answers

Answer:

a) 5.7 cm

b) 3.05 cm

Step-by-step explanation:

a)

Since BE is parallel to CD,

Then AB/AC = BE/CD

So Length of CD = 12.3/8.2 x 3.8 = 5.7 cm

b)

AB/AC = AE/AD

So length of AE = 8.2/12/3 x 9.15 = 6.1 cm

ED = AD - AE = 9.15 - 6.1 = 3.05 cm


I need help this is so confusing

Answers

Point c is quadrant 2,point T is quadrant 1,point R is x axis , point h is quadrant 3

so point C would be on Quadrant I

T on Quadrant II, H on Quadrant III and R is not really on a quadrant, the coordinate is on the X axis.

Please Hurry! I will award the first person right the brainlyest award

Answers

Answer:

y = -3

Step-by-step explanation:

When you graph it on a graphing calculator or on desmos, it appears to be at y = -3

$400 interest is earned on a principal of $2000 at a simple interest rat 5% interest per year.for how many year was the principal invested

Answers

Answer:

4 Years.

Step-by-step explanation:

Given:

Principle ⇒ 2000

Interest ⇒ 400

Rate ⇒ 5%

To Find:

Time ⇒ _

Solution:

Simple interest ⇒ p * x * t / 100

⇒ 400 = 2000 * 5 * t / 100

⇒ 400 = 200 * 5 * t / 10

⇒ 400 = 20 * 5 * t

⇒ t = 400 / 20 * 5

⇒ t = 40 / 2 * 5

⇒ t = 20 / 5

⇒ t = 4

Find a solution to the linear equation –7x+y= –28.
a

Answers

Answer:

x=4 + y/7

y= -28 + 7x

Step-by-step explanation:

Find x y and z.


please give answer as fast as possible to get marked BRAINLIEST ​

Answers

Answer:

X = 64

Y = 18

Z = 98

Step-by-step explanation:

Angles on a straight line always add up to 180 Degrees

Vertical Opposite Angles are equal to each other

X = 64

Y = 18

Z = 180 - 64 - 18 = 98

Find the probability of throwing a sum of 10 at least 7 times in 9 throws of a pair of fair dice

Answers

Answer:

19.308

Step-by-step explanation:

The probability of throwing a sum of 10 at least 7 times in 9 throws of a pair of fair dice is 0.083

What is the probability?

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

P(E) = Number of favorable outcomes / total number of outcomes

We assume that the probability of throwing a sum of 10 in a pair of fair dice is

[tex]\frac{n(5,5)(6,4)(4,6)}{n\: all\: events}[/tex]

= 3/36

= 0.083

Learn more about probability here;

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