I think you mean in terms of [tex]\sin(x)[/tex]?
Recall Euler's identity
[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]
and de Moivre's theorem
[tex]\left(e^{ix}\right)^n = \left(\cos(x) + i \sin(x)\right)^n = \cos(nx) + i \sin(nx) = e^{inx}[/tex]
where [tex]i=\sqrt{-1}[/tex].
It follows that
[tex]\sin(4x) = \mathrm{Im}\left(\cos(x) + i \sin(x)\right)^4[/tex]
By the binomial theorem, expanding the right side gives
[tex]\cos^4(x) + 4i \cos^3(x) \sin(x) - 6\cos^2(x) \sin^2(x) - 4i \cos(x) \sin^3(x) + \sin^4(x)[/tex]
and so
[tex]\sin(4x) = 4\cos^3(x) \sin(x) - 4 \cos(x) \sin^3(x)[/tex]
We can factorize this as
[tex]\sin(4x) = 4 \cos(x) \sin(x) \left(\cos^2(x) - \sin^2(x)\right)[/tex]
and using the Pythagorean identity
[tex]\cos^2(x)+\sin^2(x) = 1 \implies \cos(x) = \pm \sqrt{1-\sin^2(x)}[/tex]
this reduces to
[tex]\sin(4x) = \pm 4 \sqrt{1-\sin^2(x)} \sin(x) (1 - 2 \sin^2(x))[/tex]
B is the midpoint of AC and AC=8r-20,and AB=3x-1
Find BC
Answer:
BC = 26
Step-by-step explanation:
since B is the midpoint of AC, then AB = BC
AC = 8x - 20 & AB = 3x - 1
AC = AB + BC or 2AB
8x - 20 = 2(3x - 1)
8x - 20 = 6x - 2
subtract 6x form each side
2x - 20 = -2
add 20 to each side
2x - 20 + 20 = -2 + 20
2x = 18
x = 9
BC = 3x - 1
BC = 27 - 1
BC = 26
AC = 52
THIS IS GEOMETRY I ONLY ahve 10 MINUTES PLEASE HELP THANK U
Answer:
i need a photo or an equation TvT
Step-by-step explanation:
TvT TvT TvT
can someone help me find the area and perimeter please?
Answer:
Step-by-step explanation:
Remember that the formula to get the area of a right triangle is base times height divided by 2, so to find the area:
5 x 12 = 60/2 = 30
Area of this triangle is 30.
To find the perimeter, add all the sides:
5 + 12 + 13 = 30.
Perimeter of this triangle is 30.
cual es el resultado de -4+5/3
Answer:
English translate so i can help you ? :)
Step-by-step explanation:
What is the volume of this?
Answer:
1728 m³
Step-by-step explanation:
[tex]A_{triangle}[/tex] = [tex]\frac{7.2*4.8}{2}[/tex] = 172.8 m²
V = 172.8 × 10 = 1728 m³
HELP I forgot how to do this (show work please)
The answer is 23[tex]\sqrt{x} \pi[/tex].
Sorry that I didn't explain and made it short my annual examination is going on but I really wanted to help you.
[tex](9x2-2x+1)-(3x2+5x-8)[/tex]
Answer:
(6x² - 7x + 9)
Step-by-step explanation:
Given:
(9x² - 2x + 1) - (3x² + 5x - 8)
Find:
Value of equation
Computation:
(9x² - 2x + 1) - (3x² + 5x - 8)
(9x² - 2x + 1 - 3x² - 5x + 8)
(6x² - 7x + 9)
What is the image of ( − 3 , − 5 ) after a reflection over the x-axis?
Answer:
(-3,5)
Step-by-step explanation:
184329 rounded to the nearest 100
Answer:
184300
Step-by-step explanation:
Answer:
184300
Step-by-step explanation:
the tens place is less than 5 so the hundreds place will stay the same
(when rounding all numbers after the one being rounded will turn to 0)
The ratio of two number is 4:9.When 5 is subtracted from each of them,the new ratio becomes 3:8. Find the numbers.
Answer:
The numbers are 20 and 45
Step-by-step explanation:
Let the two numbers be a and b
The ratio of the two is 4:9
That means;
a/b = 4/9
9a = 4b •••••(i)
secondly;
Subtracting 5 from each gives a ratio of 3:8
(a-5)/(b-5) = 3/8
8(a-5) = 3(b-5)
8a - 40 = 3b - 15
3b - 15 + 40 = 8a
3b + 25 = 8a
a = (3b + 25)/8 •••(ii)
Insert this into 1
9(3b + 25)/8 = 4b
27b + 225 = 32b
32b - 27b = 225
5b = 225
b = 225/5
b = 45
From i;
9a = 4b
9a = 4 * 45
a = 4 * 45/9
a = 20
The system of equations y=-3x+2 and y=1/2x-6 is shown on the graph below
Answer:
Step-by-step explanation:
What's the question?
why is it difficult to find fossilized plants and animals in the same place
Answer: because the conditions to generate a fossil for an animal is very different from the conditions required for a plant.
Step-by-step explanation:
it is D
Answer:
d
Step-by-step explanation:
i think thats right. hope this helps
Myra is planning to purchase a recliner that costs 1,490 .the installment plan offered at the furniture store requires a 12% down payment and 20 monthly payments of $71 each .
Answer:
what is the question?
Step-by-step explanation:
Answer:
okay
Step-by-step explanation:
but whats the question tho u gave us the info so whats the question
hi guys
i need help only 19
Write the equation of the line that passes through the points (-4,8) and (-2, -1).
Put your answěr in fully reduced point-slope form, unless it is a vertical or horizontal
line.PLEASEEE HELPPP MEE
Answer:
y=-9/2x-10
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(-1-8)/(-2-(-4))
m=-9/(-2+4)
m=-9/2
y-y1=m(x-x1)
y-8=-9/2(x-(-4))
y-8=-9/2(x+4)
y=-9/2x-36/2+8
y=-9/2x-18+8
y=-9/2x-10
PLease help!! I will give brainliest for the right answer!!
Answer:
angle CDE is 10 degree
Step-by-step explanation:
As angle C is 90
Angle E is equal to angle B which is 80 (180-100)
so 90+80+X=180
X=180-170
X=10
On Monday, the baker makes 35 blueberry muffins.
What is the total number of muffins that the baker makes on Monday?
Answer:
We don't know
Step-by-step explanation:
enWe know that the baker makes 35 BLUEBERRY muffins BUT we do not know how many OTHER muffins he makes. If he just has blueberry, then he would be making 35.
Hope this helps! Have a great day :)
What is the slope of the line that contains these points? xxx -4−4minus, 4 -3−3minus, 3 -2−2minus, 2 -1−1minus, 1 yyy 222 555 888 111111
Given:
The table of values is
x y
-4 2
-3 5
-2 8
-1 11
To find:
The slope of the line that contains these points.
Solution:
From the given table consider any two point.
Let the line passes through the points (-4,2) and (-3,5). So, the equation of the line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-2=\dfrac{5-2}{-3-(-4)}(x-(-4))[/tex]
[tex]y-2=\dfrac{3}{-3+4}(x+4)[/tex]
[tex]y-2=\dfrac{3}{1}(x+4)[/tex]
Using distributive property, we get
[tex]y-2=3x+12[/tex]
[tex]y=3x+12+2[/tex]
[tex]y=3x+14[/tex]
Therefore, the required equation of line is [tex]y=3x+14[/tex].
Answer: The slope is 1/5.
Step-by-step explanation:
You can find the answer by subtracting 6-1, (5) and 0-1,(1), which shows you 1/5. (Explanation sucks, sorry)
:)
Please help?
(3×+7)+(6+9)
Answer:
3x+22
Step-by-step explanation:
Please help explain. I’ve came up with 3 wrong answers
Answer:
step 1. The volume of a cylinder (V) = (pi)R^2(h).
step 2. if the volume of a similar cylinder is 88ft^3 with R =2ft
step 3. then the cylinder with R = 5 would be (5/2)^2 bigger.
step 4. the volume of figure A is 88(5/2)^2
step 5. V = 88(5/2)^2 = 550ft^3.
worth 30 points !!!!!
Answer:
a
Step-by-step explanation:
the line model shows 2 halfs of 4/10
In the slope 3/7, the 7 indicates to
Robert nixes yellow and blue paint in the ratio of three to two if he used 12 gallons of yellow paint how many gallons of blue paint would he use
Answer: 8 gallons of blue
Step-by-step explanation:
Robert mixes the paint in the ratio:
= 3 yellow : 2 blue
If there are 12 yellow used then direct proportion can be used:
3 : 2
12 : x
Cross-multiplying will give:
3x = 24
x = 24 / 3
= 8 gallons of blue
Ms. Mathews wants to put a fence around the north, south and east sides if her square garden. The garden has an area of 100ft2. How much fencing does she need?
Answer:
30 feet
Step-by-step explanation:
3 sides of x feet each
area=x^2=100
x=10
10 x 3 = 30 feet
A dealer of electric oven sold an induction heatet at Rs.4,200 with 13% VAT to a retailer. The retailer added transportation cost of Rs.250, profit 15% and local tax Rs.150 and sold to a costumer. How much will be paid for that heater if he/she has to pay 13% VAT
Answer:
$6,619.42.
Step-by-step explanation:
Since a dealer of electric oven sold an induction heater at Rs. 4,200 with 13% VAT to a retailer, and the retailer added transportation cost of Rs. 250, profit 15% and local tax Rs. 150 and sold it to a costumer, To determine how much will be paid for that heater if the consumer has to pay 13% VAT, the following calculation must be performed:
((4,200 x 1.13) x 1.15 + 250 + 150) x 1.13 = X
((4,746 x 1.15) + 250 + 150) x 1.13 = X
(5,457.9 + 400) x 1.13 = X
5,857.9 x 1.13 = X
6,619.42 = X
Thus, the price to be paid by the consumer will be $ 6,619.42.
10 points
8. The ring system around Saturn has a diameter of 170,000 miles. Find
the circumference around the ring system, to the nearest whole number.
If Saturn diameter is 72,367 miles. What is the area of Saturn to the
nearest Whole number? *
How many solutions does the system have?
You can use the interactive graph below to find the answer.
4x – 10y = –20
6x – 15y = -30
Answer:
Infinitely many solutions
Step-by-step explanation:
Answer:
infinitely many solutions
Step-by-step explanation:
cause khan academy said so
PLSSS HELPPP !!!At least how many square feet of canvas are needed to make one cover? (Use
A 44 ft.2
B 22 ft.2
C 770 ft. 2
D 154 ft.2
Answer:
154ft.2 witch is d
Step-by-step explanation:
i just know
The graph shows the number of each size T-shirt a store currently has in stock. Which statements are true?
Choose exactly two answers that are correct.
Question 3 options:
The ratio of large to small T-shirts is about 4 to 1.
There are more than 35 small and extra small T-shirts.
There are about twice as many large T-shirts as small T-shirts.
There are fewer than 100 T-shirts in all.
Answer:
medium, extra large
Step-by-step explanation:
BRAINLIEST PLEASE
reflect...........................................
Answer:
F ( -1,4)
E (-1,2)
G (-4,5)
Step-by-step explanation:
Answer:
on what
.....................