For 0 ≤ ϴ < 2π , what are the solutions to sin2(ϴ) = 2sin2 (StartFraction theta Over 2 EndFraction)?
Answers
Answer:
Its A. I took the quiz.
Step-by-step explanation:
Soluions for the given expression in the given interval will be {0, π/2, 3π/2}.
Option A will be the answer.
Solutions of the trigonometric identites:Given expression in the question,
[tex]\text{sin}^2(\theta)=2\text{sin}^2(\frac{\theta}{2} )[/tex]
[tex][2\text{sin}(\frac{\theta}{2} )\text{cos}(\frac{\theta}{2} )]^2=2\text{sin}^2(\frac{\theta}{2} )[/tex]
[tex]4\text{sin}^2(\frac{\theta}{2} )\text{cos}^2(\frac{\theta}{2} )=2\text{sin}^2(\frac{\theta}{2} )[/tex]
[tex]4\text{sin}^2(\frac{\theta}{2} )\text{cos}^2(\frac{\theta}{2} )-2\text{sin}^2(\frac{\theta}{2} )=0[/tex]
[tex]2\text{sin}^2(\frac{\theta}{2} )[2\text{cos}^2(\frac{\theta}{2} )-1)]=0[/tex]
[tex]\text{sin}\frac{\theta}{2}=0[/tex]
[tex]\frac{\theta}{2} =n\pi[/tex]
[tex]\theta=2n\pi[/tex] [Here, n = integer]
[tex]\theta=0,\pi,2\pi.....[/tex]
Therefore, [tex]\theta=0[/tex] [Since, [tex]0\leq \theta < 2\pi[/tex]]
[tex]2\text{cos}^2(\frac{\theta}{2})-1=0[/tex]
[tex]\text{cos}\theta=0[/tex]
[tex]x=\frac{\pi}{2}+\pi n}[/tex] [Here, n = integer]
Therefore, [tex]\theta=\frac{\pi}{2},\frac{3\pi}{2}[/tex] [Since, [tex]0\leq \theta < 2\pi[/tex]]
Hence, soluions for the given expression will be {[tex]0,\frac{\pi}{2} ,\frac{3\pi}{2}[/tex]}.
Learn more to get the solutions of the trigonometric expressions here,
https://brainly.com/question/14108526?referrer=searchResults
Related Questions
A model train is traveling at a constant rate of 0.75 meter per second when Rebecca starts a stopwatch. Select the graph that represents the relationship between t, the amount of time since Rebecca started her stopwatch, and d, the total distance the train has traveled during that time.
Answers
Answer:
See Explanation
Step-by-step explanation:
Given
Rate = 0.75m/s
d = distance
t = time
Required
Select the graph that represents the given relationship
The option showing the graphs is missing. So, I'll answer the question from scratch.
We have that.
Rate = d/t (i.e. distance/time)
Substitute 0.75 for Rate
0.75 = d/t
Make d the subject
d = 0.75t
To plot the graph, we assume values for time (t)
Take t = 1
d = 0.75 * 1
d = 0.75
Take t = 6
d = 0.75 * 6
d = 4.50
So, we'll plot the graph at points
(1,0.75) and (6,4.50)
See attachment for graph
Marcela needs to find the area of a circle that
has a diameter of 30 cm.
Determine whether each expression can be used to find
centimeters
Select Yes or No for each expression.
15.70
Yes
Ο Νο
30.7
Yes
Ο Νο
152.70
Yes
Ο Νο
302.7
Yes
Ο Νο
15. 157
Yes
Ο Νο
Answers
Answer:
Step-by-step explanation:
yes no no yes
Jasper starts the month with $24 in his savings account. At the end of each week, Jasper adds
$8 to the account. Use your equation to determine how many weeks have passed when Jasper reaches $166
in his account.
Answers
Answer:
55 or 56 I think sorry if I'm wrong.
Step-by-step explanation:
connie has a cat and a dog. For every 2 cups of dog food,the cat eats 6 ounces of cat food. Based upon the given ratio of dog food to cat food, fill in the missing data to create a table of equivalent ratios.
Answers
Answer:
21
Step-by-step explanation:
24 minus 3 is 21
A transformation that changes the size or shape of a figure is
called a rigid transformation.
True
Or False
Answers
Answer:
False
Step-by-step explanation:
Find the distance between the two points rounding to the nearest tenth (if necessary).
(-9,7) and (0, -5)
Answers
Answer:
15 units
Step-by-step explanation:
distance formula is √(x-x)^2 + (y-y)^2
Answer:
15
Step-by-step explanation:
[tex]d=\sqrt{(0-(-9))^{2} + (-5-7)^{2} } \\d=\sqrt{225} \\d=15[/tex]
PLEASE HELP!! ILL MARK BRAINLYEST!!!!!!
The solution of the equation 2 d - 6 = 5 is _____.
A. 1/2
B. 1 1/2
C. -1/2
D. 5 1/2
Answers
Answer:
the answer is b
Step-by-step explanation:
Answer:
is really is B
:))))))))))))))))))))))))))))))))))))))))
0.89 is 10 times as much as
Answers
Answer:
.0089
Step-by-step explanation:
Match each power of a power expression with its simplified expression
Answers
2. (-4^9)^2 = (-4)^18
3. (4^6)^-3 = 4^-18 = 1/4^18
4. (4^0)^9 = 4^0
Answer:
answer in picture
Step-by-step explanation:
23.984 round to the nearest tenth
Answers
Answer:
24
Step-by-step explanation:
9 is in the tenths place, and because 8 is in the hundredths, we need to move 9 up one number. However, that gives us 10. So we add 1 to 23 because 10 tenths is like 1 whole number.
1+23=24
Answer:
its is 23.990
Step-by-step explanation:
A plumber charges a $50 fee plus $100 per hour to complete a plumbing job. The total amount spent on a plumbing job can be expressed by the function T(x) = 100x + 50 where x represents the number of hours spent on the plumbing job. The maximum time spent on one job per day is 8 hours. Find a reasonable domain and range for this situation.
Answers
Answer:
Between 150 and 800
T is between 150 and 800
Step-by-step explanation:
given information
charges=$50
charges per hour=$100
let the amount of time spent be x
therefore the function for the total amount is
T(x) = 100x + 50
we want to estimate the amount for 1 hour and 8 hours
for 1 hour we have
x=1
T(x) = 100x + 50
T(1) = 100(1)+ 50
T(1) = 150
for 8 hours we have
x=8
T(x) = 100x + 50
T(8) = 100(8)+ 50
T(8) = 800+50
T(8) = 850
the domain is between 150 and 800
what is the product
A: [-32 4 20 -36]
B: [32 -4 -20 36]
C: [4 -5-9 5]
D: [-32 -1 -5 9]
Answers
Answer:
A. I hope that this helps
Answer:
it is A.
Step-by-step explanation:
i took the test and got %100
Which function best describes the
number of bacteria present in the
colony on day x?
Answers
Answer:
Hello. The answer is A.
Step-by-step explanation:
Just put different x in the four formulas below and see which one will give you the correct amount.
I hope you understand.
A is the correct answer.
What the distance between (-4,2) and (-4,-4)
Answers
Answer:
6
Step-by-step explanation:
u dont even need to use the distance formula for this
u can see that the x points are both the same, so just look at the distance btwn the y values.
|2| + |-4| = 6
Help me please!!
Name the Property of Equality that justifies the statement:
If m∠A + m∠B = m∠C, then m∠A = m∠C - m∠B
A. Transitive Property
B. Symmetric Property
C. Reflexive Property
D. Subtraction Property
Answers
Answer:
Subtraction Property
Step-by-step explanation:
Subtraction Property Equality helps you to deduct the same number to get an identical equation from both sides of an equation.
Answer:
[tex]D. \: Subtraction \: Property[/tex]
Step-by-step explanation:
[tex]subtraction \: of \: a \: perticular \: value \: \\ from \: both \: sides \: of \: the \: equation.[/tex]
♨Rage♨
3 in
9 in
13 in
Surface Area =
Help also explain please
Answers
Next
Plug in 3 for length, 9 for height, and 13 for width. ( or however you’d like for width length height but only one number can be represented by h, l, and w.)
Then we add all the numbers
2(3)(13)+ 2(3)(9) + 2(9)(13) = SA (surface area)
78 + 54 + 234 = 366 in^2 or 366 sq. inches
Helpppppp pleaseeeeee!!!!
Answers
Answer:
box 1, 4 and 5 are correct
Step-by-step explanation:
Box 1 is correct if you simplify the equation by multiplying both sides by 4. When you multiply the left side by 4 you end up with 56 + 8x since 4 times [tex]\frac{1}{4}[/tex] equals 1. The right side becomes 4 x 20 = 80. So 56 + 8X = 80. If you continue to solve for X, you first have to subtract 56 from both sides of the equal sign which looks like this: 56 - 56 + 8X = 80 - 56 which reduces down to 8X = 24. Dividing both sides by 8 then reduces that equation down to X = 3.
Box 4 is also correct. When you have an equation like [tex]\frac{1}{4}[/tex] (8x + 56), you have to multiple both numbers on the inside of the parentheses by the number on the outside of the parentheses. So the equation is ([tex]\frac{1}{4}[/tex] X 8x) + ([tex]\frac{1}{4}[/tex] X 56) which results in 2x + 14. The right side of the equal sign does not change so now you have
2x + 14 = 20. To get rid of the 14 on the left, you subtract 14 from both sides.
2x + 14 - 14 = 20 - 14. On the left, 14-14=0 so you end up with just 2x. On the right 20-14=6. So now you have the equation 2x = 6. If you continue to solve for x, you divide both sides of the equal sign by 2. This will give you x = 3. Same as what you get by solving for x in Box 1 above.
Box 5 is also correct. As you see above when you solve for X in both answers above, X = 3.
What are the factors of the function represented by this graph?
y F10
48
+6
+2
H
-10
-8
-6
14
-2
2
4
6
8
10
-2
4
-6
-8
Answers
hELP MEEEEEEEEEEEEEEEE
Answers
Answer:
B
Step-by-step explanation:
We can use the rule [ x^y * x^z = x^y+z ] to simplify.
31^7 * 31^4
31^7+4
31^11
Best of Luck!
Find the solution to the equation
8n+5=23-2n
Round your answer to the nearest hundredth, if necessary
Answers
10n = 18
n = 1.8
Which property is shown? 4b + 3 + 2b + 5 = 4 b + 2b + 3 + 5*
Answers
Answer:
it is communitive
Step-by-step explanation:
because the powers or variabled both equal the first and second problem
(the firt and second term problems have to match in answer
GIVING BRANLIEST TO THE RIGHT ANSWER FOR FUN :)
The equation y = 1/2x represents a proportional relationship. What is the constant of proportionary?
A. x
B. 0
C. 1/2
D. 2
Answers
Answer:
C 1/2
Step-by-step explanation:
i need help now ........
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Answers
Answer:
Step-by-step explanation:
3 17/30
A wholesale club sells eggs by the dozen. Does the table show a proportional relationship between the number of dozens of eggs and the cost? Explain
Answers
Answer:
Answer: The table is proportional.
Step-by-step explanation: You would do 21/6 to get 3.5. Then 28/8 to get 3.5. After 35/10 to get 3.5. Finally 49/14 to get 3.5. If each answer (3.5) is the same than it is proportional.
Answer: The table is proportional.
hope dis help
5 to the power of -3 in exponential form
Answers
hope this helps
What are the coordinates of the midpoint of segment whose endpoints are A(-1,9) and B(3,8) Make sure use the decimals if necessary and write with no spaces (x,y) with you solving for x and y.
Answers
IN NEED OF HELP!! 15 POINTS!!
Answers
Answer:
D
Step-by-step explanation:
If you draw a line in the middle of the w they will look the same
Answer:
it would be letter D
Step-by-step explanation:
Your first job is to babysit a couple of times a week. You charge a flatfee of $10 for transportation back and forth to the house plus $5.50per hour. Let t be the time in hours that you babysit. Write analgebraic expression to define the amount of money you will makefor t hours of work.
Answers
Answer:
5.50t + 10
Step-by-step explanation:
Total amount of money made will sum of
transportation fees and money charged for t hours of baby siting
Given
transportation fees of back and forth to the house = $10
also given that
fees of 1 hour babysitting = $5.50
we have to find fee for t hours baby sitting ,
fees of t hours babysitting = fees of 1 hour babysitting*t
fees of t hours babysitting = 5.50t
Total amount of money made = fees of t hours babysitting + transportation fees of back and forth to the house
Total amount of money made = 5.50t + 10
Thus,
algebraic expression to define the amount of money you will make for t hours of work is 5.50t + 10
True or False: An arithmetic sequence is an exponential function with a
domain of whole numbers.
Answers
Please mark as brilliant
Write the equation of the circle with center at (1,2) that passes through the point (3,6).
Answers
Answer:
Not sure sorry!
Step-by-step explanation: