Which set of steps can be used to prove the sine sum identity, sin(x + y) = sin(x)cos(y) + cos(x)sin(y)? Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (StartFraction pi over 2 EndFraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y). Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (StartFraction pi over 2 EndFraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = sin(y) and cos(–y) = –cos(y). Use the supplementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (StartFraction pi over 2 EndFraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y). Use the supplementary relationship between sine and cosine to rewrite sin(x + y) as
Answers
Answer:
A. Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (StartFraction pi over 2 EndFraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
Step-by-step explanation:
edge
The supplementary relationship between sine and cosine
to write sin(x + y) is sin x cos y + cos x sin y. and correct steps are
Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (Start Fraction pi over 2 End Fraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
What is trigonometric equation?Trigonometric equation is an equation involving one or more trigonometric ratios of unknown angles. It is expressed as ratios of sine(sin), cosine(cos), tangent(tan), cotangent(cot), secant(sec), cosecant(cosec) angles. For example, cos2 x + 5 sin x = 0 is a trigonometric equation.
What is Sin(a + b) Identity in Trigonometry?
Sin(a + b) is the trigonometry identity for compound angles. It is applied when the angle for which the value of the sine function is to be calculated is given in the form of the sum of angles. The angle (a + b) represents the compound angle.
sin (a + b) = sin a cos b + cos a sin b
According to the question
sin(x+y)
= cos ([tex]\frac{\pi }{2} - (x+y)[/tex])
Now as (cos (x-y) = cosx cosy - sinx siny )
= Cos ([tex]\frac{\pi }{2}-x[/tex])cos(-y) - sin([tex]\frac{\pi }{2}-x[/tex])sin(-y)
By using identity sin(–y) = –sin(y) and cos(–y) = cos(y)
= Cos ([tex]\frac{\pi }{2}-x[/tex])cos(-y) - sin([tex]\frac{\pi }{2}-x[/tex])sin(-y)
= sin x cos y - cos x sin(-y)
= sin x cos y + cos x sin y
Hence, the supplementary relationship between sine and cosine
to write sin(x + y) is sin x cos y + cos x sin y. and correct steps are
Use the complementary relationship between sine and cosine to rewrite sin(x + y) as Cosine (Start Fraction pi over 2 End Fraction minus (x + y) ). Apply the cosine sum identity. Then simplify using sin(–y) = –sin(y) and cos(–y) = cos(y).
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Related Questions
A dietician is considering three food types to be served at a meal she is particularly concerned with the amount of one vitamin provided?
5 years ago
at this meal ,. One ounce of food 1 provide 8 milligrams of the vitamin , an ounce of food 2 provides 24 milligram and an ounce of food 3 provides 16 milligrams . The minimum daily requirements for vitamin is 120 milligram
a. If x equals the number of ounces of food type j served at meal, determine the equation which ensure the meal satisfies MDR exactly.
i want linear equation solution of this
Answers
Answer:
8* x₁ + 24*x₂ + 16*x₃ ≥ 120
Step-by-step explanation:
food 1 provides 8 mgrs of vitamin
food 2 provides 24 mgrs of vitamin
food 3 provides 16 mgrs of vitamin
If xj ( j = 1 ,2,3 ) is the quantity in ounces of food ( 1, 2, 3 ) then:
8* x₁ + 24*x₂ + 16*x₃ ≥ 120
Give the probability distribution for X:
x 0 1 2 3
f(x) 1/4 1/8 1/2 1/8
Find Var.
Answers
Answer:
Var(x)=1
Step-by-step explanation:
x p(x) x² x*p(x) x²*p(x)
0 1/4 0 0 0
1 1/8 1 1/8 1/8
2 1/2 4 1 2
3 1/8 9 3/8 9/8
Total 3/2 13/4
The required variance can be computed as
Var(x)=sumx²*p(x)-(sum(x*p(x)))²
Var(x)=13/4-(3/2)²
Var(x)=13/4-9/4
Var(x)=4/4
Var(x)=1
Thus, the required variance is 1.
Winter coats are marked 70% off on February 1st. if a coat costs $57.75 on January 31st, how much will it cost on February 1st.
Answers
Answer:
57.75-(57.75*0.7)=17,325
Or 100-70=30
So 57.75*0.3=17.325
Answer:
$40.425
Step-by-step explanation:
hope it helps good luck
I need help please and thank you in advance
Answers
You can buy a pack of 12 batteries
for $6. What is the unit price?
Answers
Answer:
Each battery costs .5 dollars or 50 cents
Step-by-step explanation:
6/12=.5
Answer:
total units 12
cost per unit $ 0.5000
Step-by-step explanation:
Hope this helps! :)
A survey of 800 college seniors resulted in the following crosstabulation regarding their undergraduate major and their plan of going to graduate school. Compute the row percentages.
A. Yes = 35% and No = 65% Business = 25%, Engineering = 30%, and Others = 45%
B. Yes = 48% and No = 52% Business = 31.5%, Engineering = 36.5%, and Others = 32%
Answers
Incomplete question. Attached is an image of the table.
Step-by-step explanation:
A.
Yes = 35% = [tex]\frac{280}{800} * 100 =[/tex] 35%. and No = 65% = [tex]\frac{520}{800} * 100 =[/tex] 65%
Business = 25% = [tex]\frac{70}{280} * 100 =[/tex] 25%.Engineering = 30% = [tex]\frac{84}{280} * 100 =[/tex] 30%. and Others = 45% = [tex]\frac{126}{280} * 100 =[/tex] 45%.Which statement describes the vertical asymptotes of the graph of f(x) = x2–64/8x - 64
Answers
Answer:
The graph has no vertical asymptote. or A
Step-by-step explanation:
Right on edge
For the given function f(x) = (x² -64) / (8x -64) there is no vertical asymptotes of the graph.
What is vertical asymptotes ?"A vertical asymptote is a vertical line, , which represents that invisible line approaches from either the positive or negative side, the function approaches infinity. Vertical asymptotes occur at the values where a rational function has a denominator of 0."
According to the question,
Given,
f(x) = (x² -64) / (8x -64)
= ( x- 8)(x + 8) / 8(x -8)
= (x + 8) / 8
= x/8 + 1
To find vertical asymptotes denominator = 0.
But here denominator 8 ≠ 0
Therefore,
No vertical asymptotes
horizontal asymptotes: no
slant/ oblique asymptotes: y = x/8 + 1
Hence, the graph has no vertical asymptotes.
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Aloma, a university graduate who started a successful business, wants to start an endowment in her name that will provide scholarships to ChE students. She wants the scholarship to provide $13,000 per year and expects the first one to be awarded on the day she fulfills the endowment obligation. If Aloma plans to donate $240,000, what rate of return must the university realize in order to award the annual scholarship forever?
The rate of return that the university must realize in order to award the annual scholarship forever is _____%.
Answers
Answer:
5.73%
Step-by-step explanation:
Calculation for the rate of return that the university must realize
Using this formula
Rate of return = Initial payment/(Plan to donate- Initial payment)
Let plug in the formula
Rate of return=$13,000/($240,000-$13,000)
Rate of return=$13,000/$227,000
Rate of return=0.0573*100
Rate of return =5.73%
Therefore The rate of return that the university must realize in order to award the annual scholarship forever is 5.73 %.
Analyzing a System
Solve the system of inequalities.
x² - gpg
v> 2
Which describe the solution set of the given system?
Check all that apply
The solution set is unbounded.
The point (1, 0) is in the solution set.
There is one point of intersection of the boundary
curves
The boundaries of the overlapping region are in the
solution set.
The boundary curves intersect at approximately
(-3,0).
Answers
Answer:
A, C, E
Step-by-step explanation:
took the assignment on edge
Answer:
a , c and e
Step-by-step explanation:
got it right on edg ^u^
the info about it is down below enjoy your day :)
Answers
Step-by-step explanation:
column 2 is greater
have a gret day too
Un abuelo quiere repartir una cierta cantidad de manera proporcional entre sus tres nietos de 14, 10 y 6 años de edad ¿A quién le corresponde más? Resuelve el problema apoyándote con los videos previos. Una vez resuelto, planteen el tema a alguien de su familia y juntos comenten cómo utilizan las relaciones proporcionales en sus quehaceres.
Answers
Answer:
El nieto de 14 años de edad recibirá la mayor cantidad.
Step-by-step explanation:
En este problema, debemos tener en mente que la cantidad aportada es directamente proporcional a la edad de quien recibe, esta cantidad es igual al producto de la cantidad total y la razón de la edad de quien recibe y la suma de todas las edades.
Bajo este razonamiento, podemos concluir que el nieto de 14 años de edad recibirá la mayor cantidad.
idk the answer at all
Answers
Answer:
y-1=3/2(x+3)
Step-by-step explanation:
Calculate the slope m of the given line using the slope formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (- 2, - 4) and (x₂, y₂ ) = (2, 2) ← 2 points on the line
m=2+4/2+2=6/4=3/2
Parallel lines have equal slopes.
The equation of a line in point-slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = 3/2 and (a, b) = (- 3, 1), thus
y - 1 = 3/2 (x - (- 3)), that is
y - 1 = 3/2 (x + 3) ← equation in point- slope form
Need help asap PLEASE same problem just made it easier to see
Answers
Label XY with 3.
Label angle X with 53 degrees.
Label angle Y with 90 degrees.
Label angle C with 37 degrees.
Label angle A with 53 degrees.
Label BC with 4.
Label AC with 5.
Answer: i don't know if you want degrees or the lengths so i did both
∠ACB = 37°
∠BAC = 53°
∠ZXY = 53°
∠XYZ = 90°
∠XZY = 37°
∠ABC = 90°
BC = 4
AC = 5
AB = 3
YZ = 4
XY = 3
XZ = 5
Step-by-step explanation:
37 + 90 = 127
180 - 127 = 53
37 + 90 + 53 = 180
Hanna lost 4 points on a test and earned 4 points on an extra-credit question
Answers
Answer:
the total points earned and lose cancel eachother out to be 0. she did not lose any points
Answer:
the total points earned and lose cancel eachother out to be 0. she did not lose any points
Step-by-step explanation:
hurry i'm doing a test so
what is the value of x in the equation 5.5x = 17.6?
Answers
Answer:
x=3.2
Step-by-step explanation:
Answer:
x=3.2
Step-by-step explanation:
Divide each term by 5.5 and simplify.
x = 3.2
4(3x + 1)
What is the answer to 4(3x + 1)
Answers
Divide 12 by 4
X=3
Answer:
Answer is 12x+4. Hope that helped.
Find the product: 5(2x2 + 4x + 3)
Answers
Answer:
10x^2+20x+15
Step-by-step explanation:
5(2x^2+4x+3)
u distributed it and u get
10x^2+20x+15
Answer: I am pretty sure it is 115+20x
Step-by-step explanation: You have to do distributive Property
10 times 10+ 20x+15
100+20x+15
115+20x
The product of two integers is -40. If
the sum of the two integers is -3, what
are the two integers?
Answers
Answer:
-20
Step-by-step explanation:
no cap
Sequence: 49, 36, 25, 16, 8, 4, 1 * Is this a arithmetic or geometric sequence? and if it is arithmetic find the common difference and if it is geometric find the common ratio? and please do not give me a stupid answer only smart people answer this if you know the answer to this you are smart. 1
Answers
Answer:
The given sequence [tex]49,36,25,16,8,4,1[/tex] is neither a arithmetic nor a geometric sequence
Step-by-step explanation:
A sequence is said to be an arithmetic sequence if difference between the terms is same.
A sequence is said to be a geometric sequence if ratio of the terms is same.
Given sequence is [tex]49,36,25,16,8,4,1[/tex]
Here,
[tex]36-49=-13\\25-36=-11\\36-49\neq 25-36[/tex]
So, this sequence is not an arithmetic sequence.
Also,
[tex]\frac{36}{49}\neq \frac{25}{36}[/tex]
So, this sequence is not a geometric sequence.
Therefore,
The given sequence [tex]49,36,25,16,8,4,1[/tex] is neither a arithmetic nor a geometric sequence
(HELP PLEASE) Lines a and d are
-non-coplanar.
-parallel.
-perpendicular.
-skew.
Answers
What integer represents the situation ""6 yards behind the winner""?
Answers
Answer:
-6
Step-by-step explanation:
An integer is a whole number that can either be positive, negative or zero.
Now, we want to write the integer that represents 6 yards behind the winner.
Now, a distance of 6 yards behind the winner means a deficit distance of 6 yards behind the winner. Which in turn means a negative distance which is -6 yards behind the winner.
Thus, the integer is -6
Maureen reads at an average rate of 18 pages per hour. If she reads for 3.5 hours how many pages will she read?
Answers
the answer is 63
Step-by-step explanation
18 x 3.5=63
Answer: 63 pages
Explanation: 18 times 3 equals 54 and then for half an hour that's 9 minutes added to 54 which is 63 pages.
8/9 - 1/3 equals what
Answers
Explanation: Start by making them have common denominators by multiplying the numerator and denominator by 3, so now its 8/9-3/9 then 8-3=5 so the answer is 5/9.
Find the slope of the line
Answers
HELP : calculating slope between two points.
Answers
Answer:
(1.)3.5 (2.)-3 (3)0
Step-by-step explanation:
if right comment please
1. m=7/2
2.m=-3
3.m=0
I need help please thanks
find x when y = 18, if y = 9 when x = 8
ASAP PLEASE
Answers
so
y=9 -> y=18
*2
x=8 -> x=16
*2
so x = 16
Answer:
the only logical way solving this question is:
if y=9 then x=8
if y=18 then x should be 16
Step-by-step explanation:
I cant find any other way to solve
Look at the pattern below.
0, 3, 6, 9, ...
Create a new pattern that follows the same rule as the one above.
Answers
0,5,10,15,20,
Step-by-step explanation:
I'm just adding 5 to each because I add 3 to each number
What is the midpoint of the segments with endpoints (3,7) and (9,15)
Answers
I have attached the equation so it’s easier to understand.
To find the midpoint we do
(x^1+x^2 /2 , y^1+y^2 /2)
3, 7 is x^1, y^1
And
9, 15 is x^2, y^2
(3+9 /2 , 7+15 /2)
Add the x and y =
(12/2 , 22/2)
Now we divide both by 2 =
(6, 11)
Answer:
(6,11)
I can confirm that this question is right.
12/2 22/2
(6 , 11)
To finish a certain job in 8 days in 6 workers are needed. if it is required to finish the same job in 2 days advance how many workers have to work?
Answers
Answer:
The job needs 48 worker/days.
Step-by-step explanation:
To do it in 4 days, 48/4 or 12
Use algebraic means to show that x^2 + y^2 = 8 is not a function. Explain your process.
Answers
Answer:
For a single value of x function has more than one corresponding value of y which satisfies the equation.
Step-by-step explanation:
Function: A relationship between a set of inputs and a set of possible outputs, where exactly one output is associated with each input.
It means for an equation to represent a function any single value of x there should be only one corresponding value of y which satisfies the equation.
Now consider the given equation.
[tex]x^2 + y^2 = 8[/tex]
If we put x=0 then we get two value of y i.e [tex]\sqrt8[/tex] and [tex]-\sqrt8[/tex] which satisfy the equation and therefore the equation is not a function.