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Step-by-step explanation:
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Solve for x:sinx+sin2x+sin3x=cosx+cos2x+cos3x in the interval 0≤x≤2π.
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We write the given equation as
(sinx+sin3x)+sin2x=(cosx+cos3x)+cos2x
or 2sin2xcosx+sin2x=2cos2xcosx+cos2x
or sin2x(2cosx+1)=cos2x(2cosx+1)
or (sin2x−cos2x)(2cosx+1)=0
∴sin2x−cos2x=0 or 2cosx+1=0
If sin2x−cos2x=0, then tan2x=1,
Hence 2x=nπ+π/4
or x=(4n+1)
8
π
.(1)
If 2cosx+1=0, then cosx=−1/2 (2)
∴x=2nπ±
3
2π
or x=
3
6n±2
π
We seek values of x in the interval 0≤x≤2π
In this interval (1) gives
x=π/8,5π/8,9π/8,13π/8. (n=0,1,2,3)
and (2) gives x=2π/3,4π/3. (for n=0,1)
Thus we get the answer
x=π/8,5π/8,2π/3,9π/8,4π/3,13π/8.
Related Questions
Antonio thought of a number ‘x’. He subtracted 7 from thrice the number to get 11.
Find x.
Answers
Answer:
32=X becuase you said He subtracted 7 three times or thrice so we multiply that then add 11 because it was our remaining number from subtraction. so 32
Step-by-step explanation:
HELP WILL GIVE BRAINLIEST ASAP
Answers
Answer:
I believe it's also 74°
Step-by-step explanation:
Because AGF and CGE are congruent,so the angle measurement should stay the same
Answer:
CGE is 74°
Step-by-step explanation:
AGF = FGD
FGD = CGE
AGF = EGB
AGF = 74°
FGD = 74°
CGE = 74°
EGB = 74°
360° is a circle and CGA = BGD
74 + 74 + 74 + 74 + x + x = 360
296 + 2x = 360
2x = 360 - 296
2x = 64
2x/2 = 64/2
x = 32
CGA and BGD are 32
CGE is 74°
Hope This Helps! •v•
Someone help meee?
This is soo hard
Answers
Answer:
100
Step-by-step explanation:
angles CHF and EHI are congruent angles because CD is a straight line.
Therefore EHI must be 20 degrees.
angles DIG and EIH are congruent angles because CD is a straight line.
Therefore EIH must be 60 degrees.
Now that you know two of the three angles in the triangle HEI,
Total degrees in a triangle - EIH - EHI = HEI
180 - 60 - 20 = 100
What is the midpoint of the segment that joins the complex numbers 7 + 3i and -5 – 8i?
A) 16+11/2i
B) (1,5/2)
C) 1- 5/2i
D) (-6, 11/2)
Answers
Answer:
C)
Step-by-step explanation:
The midpoint is the average of the two points.
Thus,
Midpoint = [ ( 7 + 3i) + (-5 - 8i) ] / 2 = ( (7-5) + i(3-8) ) / 2 = (2 - 5i)/2 = 1 - 2.5i
pls help me on this thank you
Answers
Answer:
C) y+6=-2(x-4)
Step-by-step explanation:
standard form of (x+4)(x-6
Answers
x^2 - 6x + 4x - 24
X^2 - 2x - 24
how much is 40+ 12= and 34=23=34=45=4=
Answers
Answer:
52 and 150?
Step-by-step explanation:
40+12=52
34+23+34+45+4
Simplify: 57+34+49
Simplify: 91+49
Add: 140
uhhhhhhhhhhhhhhhhhhhhhh
Answers
Answer:
Caaaaannnnnn''ttttttttt seeeee iiiiiitttttt
explain how and solve please asap !
Answers
3y = 123
y = 41
x is slightly less trivial but also simple:
123 + 4x + 1 = 180
4x = 56
x = 14
Answer:
x=14
y=41
x+y= 55
Step-by-step explanation:
Since a and b are parallel you know that 123° and 3y are the same degree, so 123 divided by 3 because its 3×y= 41 so y=41
the line123° and 4x+1 are on has to equal 180 because its a straight line, 180-123= 57. 57- 1 because its not with the x= 56. 56÷4 because its 4×x/its with the x= 14. Hope thsi helps :)
jada has $20 to spend on games and rides at a carnival. Games cost $1 each and rides are $2 each.
which equation represents the relationship between the number of games, x , and the number of rides, y,
that Jada could do if she spends all her money?
A: x + y =20
B: 22 + 4 = 20
C: 0+2y=20
Answers
Answer:
I believe its A
Step-by-step explanation:
Hope it helps
four hundred five times seventy
Answers
Answer:
Step-by-step explanation:
28350, two thousand and eight, three hundred and fifty
Answer:
28350
Step-by-step explanation:
whats 7 squared ....................................................
Answers
Answer:
[tex]49[/tex]
Step-by-step explanation:
[tex]→7×7[/tex]
[tex]→49[/tex]
Drag a statement or reason to each box to complete this proof.
Given: the measure of angle A C D equals 60 degrees. Prove: triangle A B C is an obtuse triangle. Art: A triangle A B C. Side B C of the triangle is extended as a ray through point D.
--
check images below!
Answers
Answer: 2. Linear pair postulate
4. 60 + mACB=180
5. mACB=120
6. definition of obtuse angle
The value of straight angle ∠BCD = 180° thus the angle ∠ACB = 180°- 60° = 120° therefore, the given triangle ABC is the obtuse triangle.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given triangle ABC with extended line CD.
Since CD is colinear with BC, therefore, BCD will be a single straight-line segment.
The ∠BCD is straight angle so it will be 180°.
∠BCD = ∠ACB + ∠ACD
∠ACB + 60 = 180
∠ACB = 180 - 60 = 120°.
An obtuse triangle is a triangle whose one or more interior angle is greater than 90°.
Since∠ACB > 90° therefore triangle ABC is an obtuse angle.
Hence "The value of straight angle ∠BCD = 180° thus the angle ∠ACB = 180°- 60° = 120° therefore, the given triangle ABC is the obtuse triangle".
For more about triangles,
https://brainly.com/question/2773823
#SPJ5
The set of all possible outputs for a function is its:
Answers
Answer:
the set of all possible outputs for a function is the range
30 POINTS AND BRAINLEST FOR ANSWER HELP!!!!!
Answers
Answer:
a
Step-by-step explanation:
A plant grows 3/8 inch every month. How many inches
does the plant grow in 10 months?
© ?
0 10
Answers
Answer:
B. 3 3/4
Step-by-step explanation:
3/8 * 10 = 30/8
30/8 = 3 3/4
need help pls thx..........
Answers
Answer:
170 degree. is the answer
Plz answer quick giving brainliest
Answers
Please mark brainelist
What is the distance between 3 and 1?
Answers
Answer:
2
Step-by-step explanation:
Answer: 2
Step-by-step explanation:
A racing car on the straight accelerates from 100 km/h to 316 km/h in three seconds.
What is its acceleration?
Answers
Answer:
The acceleration of a car that travels in a straight line at a constant speed of 100 km/h is zero. Average.
Which expression(s) are equivalent to -12.48 Show me how to do it pls
-416 x 0.3.
-3 x 41.6.
-4.16 x 3
All of the above
Answers
Answer:
C. -4.16 x 3Step-by-step explanation:
Find the values of expressions and compare with -12.48:
-416 * 0.3 = -124.8 ≠ -12.48, No-3 * 41.6 = -124.8 ≠ -12.48, No-4.16 * 3 = - 12.48, Yes#1
-416(0.3)-12.48Yes
#2
-3(41.6)-124.8No
#3
-4.16(3)-12.48Yes
Two sides of a triangle have lengths 6 and 16. Which inequalities represent the possible
lengths for the third side, x?
Answers
Answer:
22 > x > 10
Step-by-step explanation:
By the triangle inequality, the length of the 3rd side must be less than the sum of the two other sides and greater than the positive difference of the other two sides. Thus, 6 + 16 > x > 16 - 6
22 > x > 10
You receive an inheritance of $15,500, and you place the full amount into a bank account. The bank pays a simple interest rate of 7.5% per year. How much interest have you earned after three years?
Round your answer to the nearest dollar.
Do NOT round until you have calculated your final answer
Answers
Meaning the final answer is $3,756.
what is the best way to explain graphing
Answers
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. ... We then represent the data using a bar graph. The number of each of the supplies is represented with bars. The more the height of the bar, the more is the number of the supply or item used.
Answer:
In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner.
Step-by-step explanation:
Dilations of a triangle are congruent to the original triangle.
Answers
Answer:
origanal
Step-by-step explanation:
origanaol
10.
Match the graph with the correct equation.
A. y + 3 = –(x + 5)
B. y – 5= –(x + 3)
C. y – 3 = (x + 5)
D. y – 3 = –(x + 5)
Answers
Answer:
D. y - 3 = -(x + 5)
Step-by-step explanation:
I used a calculator called m.a.t.h.w.a.y !
Answer:
D. y – 3 = –(x + 5)
Step-by-step explanation:
Graph the line using the slope and y-intercept, or two points.
Slope:
−
1
y-intercept:
(
0
,
−
2
)
x
y
0
−
2
1
−
3
Graeme is inviting 7 friends to a party.Each friend wants 4 cookies and each box has 12 cookies. How many boxes should Graeme get?
Answers
Answer:
Graeme should get 3 boxes
Step-by-step explanation:
hope this helped!
you got this dont ever give up all of you are so so smart!!
3. Dean has these cans of soup in his kitchen cabinet: 2 tomato, 3 chicken, 2 cheese, 2 potato, 1 beef. Dean will randomly choose one can of soup. Then he will put it back and randomly choose another can of soup. What is the probability that he will choose a can of beef soup both times? *
Answers
Answer:
2/20 or 0.1
Step-by-step explanation:
So we are given this data:
Tomato = 2
Chicken = 3
Cheese = 2
Potato = 2
Beef = 1
Total Chances (Sum Of All)
Total = 10
Beef is 1
To get beef soup one time it would be 1/10
what about 2 times
we can just multiply by 2*
so 1 / 10 * 2 = 2 / 20 or 0.1
The Answer would be 2/20 or 0.1
Given the Quadrilateral pictured below. What is the
value of "X"?
Answers
Answer:
Value of x is used to consider unknown value.
Step-by-step explanation:
Value of x is used to consider unknown value. The letter “x” is commonly used in algebra to indicate an unknown value. It is referred to as a “variable” or, in some cases, a “unknown.” In x + 2 = 7, x is a variable.
Solve for x step by step: 2(n+5)=-2
Answers
Step 1: Simplify both sides of the equation.
(2)(n) + (2)(5) =-2
2n + 10 = -2
Step 2: Subtract 10 from both sides.
2n+10−10=−2−10
2n = -12
Step 3: Divide both sides by 2.
2n/2 = -12/2
N=-6