Choose a justification for each step in the derivation of the sine difference identity.
Step 1:
Step 2: Distributive property
Step 3: Associative property
Step 4: Factoring out –1
Step 5:
Step 6:
Step 7:
Answers
The Sine difference function was derivated with the help of the sine sum function.
What is the sine difference function?The difference function for the sine function states that the sine of the difference of two angles equals the product of the sine of the first angle and cosine of the second angle minus the product of the cosine of the first angle and the sine of the second angle.
As we know that
[tex]Sin(a+b) = SinaCosb + CosaSinb[/tex]..........(1)
If we replace b by -b equation (1) becomes
[tex]Sin(a+(-b)) = SinaCos(-b) + CosaSin(-b)[/tex]
We know that
Cos(-b) =cosb
Sin(-b) =-Sinb
So, [tex]Sin(a-b) = SinaCosb -CosaSinb[/tex]
Therefore, the Sine difference function was derivated with the help of the sine sum function.
To get more about the Sine function visit:
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Related Questions
A rock is 7 feet below the surface of a river. If its position can be recorded as -7, what would the position of 0 represent?
A. On the surface of the river
B. At the bottom of the river
C. 7 feet above the surface of the river
D. 7 feet below the surface of the river
Answers
Solve the equation 186+10x=25.5x to find how many diving lessons x Jacy can take for the cost to be the same with and without a membership.
__ lesson(s)
Answers
Answer:12 lessons
Steps in image below:
The number of lessons that take for the cost to be the same with and without a membership will be 12.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The equation is given below.
186 + 10x = 25.5x
Simplify the equation, then we have
25.5x - 10x = 186
15.5x = 186
x = 186 / 15.5
x = 12
The number of lessons that take for the cost to be the same with and without a membership will be 12.
More about the solution of the equation link is given below.
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Find the missing side lengths of each triangle.
Answers
4d - 13 = 12 - d
5d = 25
d = 5
hence,
LK = d + 6
= 5 + 6
= 11
what is Negative 5 and StartFraction 5 over 8 EndFraction + 3 and one-half
Negative 3 and StartFraction 1 over 8 EndFraction
Negative 2 and one-half
Negative 2 and StartFraction 1 over 8 EndFraction
Negative StartFraction 7 over 8 EndFraction
Answers
Answer:
its c
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
i got it right
12,400 × [] = 124
What number should go in the box to make the equation true?
Answers
Answer:
100
Step-by-step explanation:
inverse operation: 12,400 divided by 124
trying this again not sure if it went through the first time
Answers
The picture is really blurry for me. I can't read it...
Solve the following system of equations:
Y=x^2+4x+4
Y=x+2
What is the value of y?
Answers
Answer:
y=4, y=2
Step-by-step explanation:
By Factoring And Using Quadratic Formula x raise to two minus 10x is equals to negative 21
Answers
Answer:
[tex]x =3[/tex] or [tex]x = 7[/tex]
Step-by-step explanation:
Given
[tex]x^2 - 10x = -21[/tex]
Required
Solve by factoring & quadratic formula
By Factoring:
[tex]x^2 - 10x = -21[/tex]
Equate to 0
[tex]x^2 - 10x +21 = 0[/tex]
Expand:
[tex]x^2 - 7x -3x+21 = 0[/tex]
Factorize:
[tex]x(x-7)-3(x-7) = 0[/tex]
[tex](x-3)(x-7) = 0[/tex]
[tex]x -3 = 0[/tex] or [tex]x - 7 = 0[/tex]
[tex]x =3[/tex] or [tex]x = 7[/tex]
By quadratic
[tex]x^2 - 10x = -21[/tex]
Equate to 0
[tex]x^2 - 10x +21 = 0[/tex]
For
[tex]ax^2 + bx + c = 0[/tex]
x is solved using:
[tex]x = \frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
where
[tex]a = 1[/tex]; [tex]b = -10[/tex]; [tex]c = 21[/tex]
So:
[tex]x = \frac{-(-10)\±\sqrt{(-10)^2-4*1*21}}{2*1}[/tex]
[tex]x = \frac{10\±\sqrt{100-84}}{2}[/tex]
[tex]x = \frac{10\±\sqrt{16}}{2}[/tex]
[tex]x = \frac{10\±4}{2}[/tex]
Split
[tex]x = \frac{10+4}{2}[/tex] or [tex]x = \frac{10-4}{2}[/tex]
[tex]x = \frac{14}{2}[/tex] or [tex]x = \frac{6}{2}[/tex]
[tex]x = 7[/tex] or [tex]x =3[/tex]
A section of a railway has a slope of approximately 0.47. In this section, a vertical change of 1 unit corresponds to a horizontal change of what length? Round your answer to the nearest hundredth.
Answers
Step-by-step explanation:
A slope of 0.47 means that, for every 100 feet of horizontal change, the vertical rise = 47 feet
We can use a proportion here
0.47 / 1 = 1 / x
Cross-multiply
0.47x = 1*1
0.47x = 1
Divide both sides by 0.47
x = about 2.13 units
Answer the question please:
The correct answer will be marked as brainliest =)
thanks xoxo
Answers
Answer:
The answer is 5^-4.
Hope this helps and if you could mark this as brainliest. Thanks!
Answer:
[tex]\frac{1}{5^{4}}[/tex]
Step-by-step explanation:
[tex]\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}},[/tex] if n >m
[tex]\frac{5^{3}}{5^{7}} = \frac{1}{5^{7-3}}=\frac{1}{5^{4}}[/tex]
I forgot how to simplify like this can someone explain to me how i do this?
Answers
Answer:
Just subtract 11 from 7.
Answer:
-4
Step-by-step explanation:
WUTS THE ANSWER IM SO LOST I NEED HELP!!! :(
Answers
1/6 = 0.16 acres in 8 minutes.
--
0.16 ÷ 8 = 0.02 acres mowed in 1 minute.
--
(60 minutes in an hour)
0.02 x 60 = 1.2 acres mowed in an hour.
--
1.2 is equal to 1 1/5, and jami needs to mow 1 1/2 acres. so no, jami cannot mow 1 1/2 acres in an hour.
Hannah needs to calculate the cotangent of an angle. She uses the ratio
opposite leg
for her calculation. Did Hannah correctly calculate the cotangent of the angle?
adjacent leg
A
B.
Yes, Hannah correctly calculated the cotangent of the angle.
adjacent leg
No, Hannah should have used the ratio
opposite leg
hypotenuse
No, Hannah should have used the ratio
opposite leg
O c.
D.
No, Hannah should have used the ratio
adjacent leg
hypotenuse
Answers
Answer:
B. No, Hannah should have used the ratio [tex] \frac{adjacent}{opposite} [/tex]
Step-by-step explanation:
✍️The formula for calculating cotangent of an angle is given as:
[tex] cot = \frac{adjacent}{opposite} [/tex].
The ratio, [tex] \frac{opposite}{adjacent} [/tex], used by Hannah is the formula for calculating tangent of an angle.
Therefore, Hannah did not calculate the cotangent of the angle correctly.
She should have used, the ratio, [tex] \frac{adjacent}{opposite} [/tex] instead.
divide 25/1658 To find the quotient, start by dividing _
into _.
Answers
Answer:
To find the quotient, you must start by dividing 25 into 1,658.
Step-by-step explanation:
-1
A line's y-intercept is 0, and its slope is
20
What is its equation in slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Submit
Answers
Answer:
y=20x
Step-by-step explanation:
do do I intercept a zero, so you don't have a "b"
The slope is 20. that's pretty self-explanatory
could someone help me with slope cause I am struggling a little bit
Answers
Answer:
mmmmmmmmm sus
Step-by-step explanation:
There are 36 tickets sold for a raffle for the Student Art Auction, and there are two prizes to be awarded. Dionte buys two tickets, find the probability that he will win both pris(Round your answers to five decimal places.)
Answers
Given :
There are 36 tickets sold for a raffle for the Student Art Auction, and there are two prizes to be awarded.
Dionte buys two tickets.
To Find :
The probability that he will win both price.
Solution :
Number of prizes available, p = 2
Probability of getting price from first draw :
[tex]P_1=\dfrac{2}{36}\\\\P_1=\dfrac{1}{18}[/tex]
Probability of getting price from second draw if he won first prize :
[tex]P_2=\dfrac{2-1}{36-1}\\\\P_2=\dfrac{1}{35}[/tex]
So, probability of winning both prize :
[tex]P=P_1\times P_2\\\\P=\dfrac{2}{36}\times \dfrac{1}{35}\\\\P=0.00159[/tex]
Therefore, probability of winning both prize is 0.00159 .
Hence, this is the required solution.
what is the greatest common factor of 10 & 12,17 & 51,78 & 48,11 & 55,88 & 66,95 & 38,6 & 27,56 & 49,60 & 45,42 & 63,38 & 40,81 & 54,40 & 80,46 & 69
Answers
yeah baby girl it will be best for you to look that up on Google
Please help this is due tonight my future depends on it.
PROBLEM:
The cost of a pizza varies directly as the square of its radius. If a pizza with a 1 inch radius costs
$3.25, how much should a pizza with a 6 inch radius cost?
Answers
Answer:19.5
Step-by-step explanation:
3.25x6
Answer:
$19.50
Step-by-step explanation:
3.25*6
=19.50
PLS HELP ME ASAPP!!! :((
Which situation represents a proportional relationship?
A. The cost of purchasing grapefruit for $ 1.80 per pound with a coupon for $ 1.00 off the total cost
B. The cost of purchasing a basket of oranges for $1.30 per pound plus $5.00 for the basket
C. The cost of purchasing apples for $1.75 per pound plus a shipping fee of $0.16 per pound
D. The cost of purchasing peaches for $7.00 per box of peaches with a delivery charge of $3.00
Answers
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Ratio and Proportion.
C.) The cost of purchasing apples for $1.75 per pound plus a shipping fee of $0.16 per pound.
is the Correct answer.
Option C.)
Answer:
D.) The cost of purchasing peaches for $7.00 per box of peaches with a delivery charge of $3.00
Step-by-step explanation:
Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".
2(t+1)=10 what does t equal
Answers
Answer:
t = 4
Step-by-step explanation:
1. 2*t = 2t
2. 2*1 = 2
3. 2t+2 = 10
4. 10-2 = 8
5. 2t = 8
6. 8/2 = 4
7. t = 4
Answer:
t = 4
Step-by-step explanation:
2(t + 1) = 10
2t + 2 = 10
2t = 10 - 2
2t = 8
t = 8 ÷ 2
t = 4
-TheUnknownScientist
if you want brainiest than come here
go to remind.com then log in as student then put the class code: c26kda4
Answers
1. 7.35 x 10 6 – 9.42 x 10 8
2. 3.14 x 10 -3+1.59 x 10 -1
3. (2 .8x 10 -9 )(4.75 x 10 -3 )
plz hurry
Answers
In a survey of 3400 people who owned a certain type of car 2210 people said they would buy the type of car again what percent of the people surveyed were satisfied with the car? Plz help me! :)
Answers
2210/3400 is .65, move the decimal 2 to the right
Solve the formula for the specified variable.
f=m+n+p/2
pls hurry I need help
ill give brainliest
Answers
Answer:Given equation as
x-2/2=m+n
1) x=2(m+n)+2
2)h=2A/b
3) 23
4)-81
5) 17/7
6) 8
7) 4 hours
8) width is 4.5 length is 7.5
9) got wrong didn't answer
10) got wrong picked never true
11) two points I only got 1 I picked you overdrew on the account by 36.00 so I guess the other is the acount has a balance less than
Step-by-step explanation:
In this we have to isolate x. So for this firstly we will multiply both side of equation by 2.
Now we can add 2 in both side
How do you make a word problem out of an equation? (ex:Create a word problem that defines the following equation: 129+3x=1,000)
Answers
Answer:
I think of a number and multiply it by three, when I add it with 129 my answer will be equal to 1000. what is the number
HELP ASAP WILL GIVE BRAINLEIST
Solve for x in the diagram below
Answers
Answer:
X=20 3x=60
Step-by-step explanation:
a straight line is 180
180-100=80
4x=80
x=20
We can create a equation to solve for x here.
We will use the following equation:
100 + 3x + x = 180How to solve it step-by-step
[tex]100 + 3x + x = 180\\\\100 + 4x = 180\\\\4x = 80\\\\x = 20[/tex]
the price of a televison 245 . the sales tax is 8%. what is the amount of sales tax?
Answers
Answer:
the sale tax is 19.60
Step-by-step explanation:
245*0.08=19.60
Answer:
19.6
Step-by-step explanation:
8 percent *245 =
(8:100)*245 =
(8*245):100 =
1960:100 = 19.6
After taking the interest formula (I=Prt) and solving the equation for t, how many years will it take to earn $80 in interest (I) if I initially invest $500 (P) and my interest rate (r) is 4%? (Don't forget to change your percentage to a decimal!)
t=
Answers
Answer:
hehehe
Step-by-step explanation:
hehehe
A family ordered two pizzas for dinner. They ate 1/2 of the first pizza and
1/4 of the second pizza. How much more of the first pizza did they eat?
A)1/2
B)1/4
C)1/8
D)3/4
Answers
Answer:
they ate 3/4 part of pizza
Step-by-step explanation:
=1/2+1/4
=1×2/2×2 + 1/4
=2/4+1/4
=3/4
Answer:
B) 1/4 because if the pizzas have 8 slices then 1/4=2 slices and 1/2=4 slices 4-2=2 and 2 slices equal 1/4 of the pizza.
Step-by-step explanation:
Hope it helps!
Have a good day/night :)
Brainliest pls?