Determine all solutions to the equation 1 over sine theta equals 2 times sine theta on the interval [0, 2π).

Determine All Solutions To The Equation 1 Over Sine Theta Equals 2 Times Sine Theta On The Interval [0,

Answers

Answer 1

The solution to the trigonometric equation in the interval is given by:

[tex]x = \frac{\pi}{4}[/tex]

What is the trigonometric equation?

In this problem, the equation is given by:

[tex]\frac{1}{\sin{\theta}} = 2\cos{\theta}[/tex]

Applying cross multiplication, we have that:

[tex]2\sin{\theta}\cos{\theta} = 1[/tex]

Applying a trigonometric identity, we have that:

[tex]\sin{2x} = 1[/tex]

We have that on the interval [0, 2π), [tex]\sin{\left(\frac{\pi}{2}\right)} = 1[/tex]

Hence:

[tex]\sin{2x} = 1[/tex]

[tex]\sin{2x} = \sin{\left(\frac{\pi}{2}\right)}[/tex]

[tex]2x = \frac{\pi}{2}[/tex]

[tex]x = \frac{\pi}{4}[/tex]

For [tex]\frac{3\pi}{4}[/tex], we have that:

[tex]\sin{2x} = \sin{\left(\frac{3\pi}{2}\right)} = -1[/tex]

Hence only the first solution is correct.

More can be learned about trigonometric equations at https://brainly.com/question/24680641


Related Questions

8.If 20 is 50% of a number, what is the number​

Answers

20 is 50% of 40
50% of 40= 20

Percentage

100:50 x 20 = 40

The width, W , of a rectangle is 4 less than 6 times the length, which would find the area.
Group of answer choices

Answers

Solution:

Note that:

W = 6L - 4Area = LW

Substitute the value of W into the formula (Area = LW).

Area of rectangle = LWArea of rectangle = L x WArea of rectangle = L x (6L - 4)Area of rectangle = L(6L - 4)

Option C is correct.

There are 21 students in class. The median age of the students is 23. The oldest student is 29

Please explain

Answers

Answer:

At least one student is 23: Must be true

Some students are younger than 15: Could be true

Step-by-step explanation:

Statement 1: A median is a number in the middle for ex. 1, 2, 3, 4, 5 in this example 3 is the median. Another ex could be 1, 2, 3, 4, 5, 6. This time you would have to add (3 + 4), divide by 2, which equals 3.5.

Since there are 21 students in class making it an odd number 23 must be true.

Statement 2: Based on the information I am given, I would say could be true because the difference between the oldest and the median is 29 - 23 = 6 so it could be true.

Answer:

1) At least one (the 11th) student is 23 (years old), Must be true

2) Some students are younger than 15 Could be true

Step by step explanation:

1) The given parameters are;

The number of student in the class = 21

The median age of the student = 23

The age of the oldest student = 29

Therefore, given that the median age = The age of the (n + 1)/2 the student

Where;

n = The number of student in the class = 21

The median age = The age of the (21 + 1)/2 th = 11 th student, when the age of the students are arranged in increasing order, therefore, we have;

At least one (the 11th) student is 23 (years old), Must be true

2) Given that there are 10 students with ages equal to or lower than the  median age, and the difference between the median age and the age of the oldest student = 29 - 23 = 6 years, we have;

Some students are younger than 15 Could be true

Which of the following is the inverse of p → ~q?

Answers

Answer:

K/q = p if you're taking about the inverse proportions

Give answer as positive exponent

Answers

[tex]\huge\textbf{Hey there!}[/tex]

[tex]\mathsf{x^4\ \bullet \ x^{-7}}\\\\\mathsf{\rightarrow x\bullet x\bullet x\bullet x (\dfrac{1}{x\bullet x \bullet x \bullet x\bullet x \bullet x \bullet x})}\\\\\mathsf{\star \heartsuit \ - 7 = \bf -3 \ \star \heartsuit}\\\\\mathsf{\rightarrow \dfrac{1}{x\bullet x \bullet x}}\\\\\mathsf{\approx \dfrac{1}{x^3}}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{\dfrac{1}{x^3}}}}\huge\checkmark[/tex]

[tex]\huge\textbf{Good luck on your assignment \& enjoy}\\\huge\textbf{your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Anyone know answers to these? I don’t understand these at all

Answers

Answer:

[tex]\red{ m\angle B= 121\degree}\\\\\purple{AD=23\: units}[/tex]

Step-by-step explanation:

Quadrilateral ABCD is a parallelogram.

opposite angles of a parallelogram are equal in measure.

[tex]\implies (10x-19)\degree=(9x-5)\degree[/tex]

[tex]\implies 10x-19=9x-5[/tex]

[tex]\implies 10x-9x=19-5[/tex]

[tex]\implies x=14[/tex]

[tex]m\angle B= (9x-5)\degree[/tex]

[tex]\implies m\angle B= (9*14-5)\degree[/tex]

[tex]\implies m\angle B= (126-5)\degree[/tex]

[tex]\huge\implies m\angle B= 121\degree[/tex]

Opposite sides of a parallelogram are equal.

3y - 1 = y + 15

3y - y = 15 + 1

2y = 16

y = 16/2

y = 8

AD = 3y - 1 = 3*8 - 1 = 24 - 1

AD = 23

2 2/5 divided by 2 1/10

Answers

firstly let's convert the mixed fractions to improper fractions and then divide.

[tex]\stackrel{mixed}{2\frac{2}{5}}\implies \cfrac{2\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{12}{5}} ~\hfill \stackrel{mixed}{2\frac{1}{10}}\implies \cfrac{2\cdot 10+1}{10}\implies \stackrel{improper}{\cfrac{21}{10}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{12}{5}\div \cfrac{21}{10}\implies \cfrac{12}{5}\cdot \cfrac{10}{21}\implies \cfrac{120}{105}\implies \cfrac{8}{7}\implies 1\frac{1}{7}[/tex]

Answer:

first make them improper fractions

2 2/5 = 12/5

2 1/10 = 21/10
now set them up

12/5 divided by 21/10

make 21/10 a reciprocal(flip the fraction upside down)  and multiply across

12/5 x 10/21 = 1.14 or 1 1/7

[tex]5+2x^{2} +x+3x^{2} +7+6x[/tex]

Answers

Answer:

Don't know the answer but good luck?

Step-by-step explanation:

NEED HELP ASAP

Which statement correctly explains the association in the scatter plot?

Answers

Answer:

Negative relationship

Step-by-step explanation:

It is going in a negative direction.

Pls mark brainliest :)

What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale. * 12 3 X W3 x 12 Z Y Your answer ​

Answers

Answer:

What is the length of the altitude drawn to the hypotenuse?, Corollary: The length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.

Furthermore, When an altitude is drawn to the hypotenuse of a given right triangle the new figure comprises two similar right triangles?, Theorem 62: The altitude drawn to the hypotenuse of a right triangle creates two similar right triangles, each similar to the original right triangle and similar to each other. Figure 2 shows the three right triangles created in Figure . They have been drawn in such a way that corresponding parts are easily recognized.

Finally,  When the altitude is drawn to the hypotenuse of a right triangle three similar triangles are formed?, The Inscribed Similar Triangles Theorem states that if an altitude is drawn from the right angle of any right triangle, then the two triangles formed are similar to the original triangle and all three triangles are similar to each other. Perpendicular lines are lines that intersect at a 90^{circ} angle.

Step-by-step explanation:

what's the slope
(1, 1)
(3, 4)

Answers

Answer:

y= 3/2x-1/2

Step-by-step explanation:

Answer:

3/2 or 1.5

Step-by-step explanation:

gradient = ∆y/∆x

∆y = 4 - 1 =3

∆x = 3 - 1 = 2

∆y/∆x = 3/2

7. 65 out of 105
Simplify

Answers

Answer:

13/21

Step-by-step explanation:

65/105 = 13/21

Ms. Jacobi writes the equation x+y=z. If x = 5, y = 3, and z = 53,
is the equation true? Explain your reasoning.

Answers

Answer:

no

Step-by-step explanation:

Because if we substitute the value of x,y and z we get

x+y=z

5+3=53(FALSE)

Answer and Step-by-step explanation:

No, this equation is not true. But in order to show this, we need to write out the equation. So if x = 5, and y = 3, then the equation for this equation would look like this:

5 + 3 = 8.

That is incorrect because 5 + 3 does not equal 53. This is a trick question that is trying to trick you. Now if that 5 was a 50, then this equation would be true.

So, 5 + 3 ≠ 53.

I hope that this helps.

Use the model below to calculate
2
3
×
3
4
.

A rectangle is shown divided into 3 rows and 4 columns. 3 of the 4 columns are shaded blue.

A.
3
12
or
1
4
B.
12
12
or
1
C.
4
12
or
1
3
D.
6
12
or
1
2

Answers

Answer:

D

Step-by-step explanation:

i already did the test

Answer:

d

Step-by-step explanation:

A standard pair of six-sided dice is rolled. What is the probability of rolling a sum less than or equal to 8? Express your answer as a fraction or a decimal
rounded to four decimal places.

Answers

Answer:

2/3

Step-by-step explanation:

GIVING BRAINIEST IF CORRECT!!!


Farmer Taja needs a field for her horses to graze. She found a field that has a width of x+4. The length of the field is more than twice the width. What is the area of the field Taja found?

Answers

Given :

w = x + 4L = 3+ 2(w) = 3 + 2 (x + 4)

Solution:

Area = L × WArea = [3 + 2 (x + 4) ]× x + 4Area = [3 + 2x + 8] × x + 4Area = [2x + 11] × x + 4Area = 2x² + 11x + 8x + 44Area = 2x² + 19x + 44

hope it helped!

A welder needs a piece of half inch pipe 14 3/8 inch long. She has a peace that is 25 1/16 inch long how much must she cut off from the longer piece?

Answers

well, the longer piece is clearly the latter, so let's firstly convert the mixed fractions to improper fractions and then subtract.

[tex]\stackrel{mixed}{14\frac{3}{8}}\implies \cfrac{14\cdot 8+3}{8}\implies \stackrel{improper}{\cfrac{115}{8}} ~\hfill \stackrel{mixed}{25\frac{1}{16}}\implies \cfrac{25\cdot 16+1}{16}\implies \stackrel{improper}{\cfrac{401}{16}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{401}{16}~~ - ~~\cfrac{115}{8}\implies \implies \cfrac{(1)401~~ - ~~(2)115}{\underset{\textit{using this LCD}}{16}}\implies \cfrac{171}{16}\implies 10\frac{11}{16}[/tex]

You have been sent to grocery shop. They gave you $25.00 and the list of what
you need to buy, would you need more money or would you have enough money?

Here is the grocery list:
2 pounds of ham: $4.59/pound
3 bags of chips: $3.00/bag
2 loaves of bread: $1.99/loaf

Please calculate the above and write down how much it equals and what you will
have left after you buy it.

Answers

Answer:

you would have $2.98 left

Step-by-step explanation:

$4.59 x 2=9.18

3.00 x 3=9.00

$1.99 x 2=3.98

$9.18+$9.00+$3.98=22.16

$25.00-$22.16 = $2.89

3/10 of a bag of jelly beans 2/10 and of the bag were orange. What fraction of the bag was red and orange

Answers

Answer:

1/2 of the bag would be red and orange.

Step-by-step explanation:

if 3/10 of the bag was red

and 2/10 was orange, then all you have to do is the add the number of jelly beans that are red and orange,

3/10 + 2/10 is 5/10

simplify and that will get you to 1/2

Answer:

Step-by-step explanation:

if 3/10 of the bag was red

and 2/10 was orange, then all you have to do is the add the number of jelly beans that are red and orange,

3/10 + 2/10 is 5/10

simplify and that will get you to 1/2

there are 3 piles papers on a desk each pile has 21 papers how many papers are there total

Answers

Answer:

63 papers total.

Step-by-step explanation:

3 piles, 21 papers a pile, 3*21 =63.

Answer:

63

Step-by-step explanation:

because 3x21 is 63

what does a(b-c) = to?

Answers

Solution:

The expression "a(b-c)" is an example of distributive property. To simplify it, simply multiply a by the terms inside the bracket.

Simplifying the distributive property.

=> a(b - c)=> (a x b) + (a x -c)=> ab - ac

Hence, the simplified expression is ab - ac.

We can use the distributive law to simplify it or factor it but more

[tex]\\ \tt\hookrightarrow a(b-c)[/tex]

[tex]\\ \tt\hookrightarrow a(b)-a(c)[/tex]

[tex]\\ \tt\hookrightarrow ab-ac[/tex]


The price of a technology stock has risen to $9.77 today. Yesterday's price was $9.68. Find the percentage Increase. Round your answer to the nearest tenth of a percent.

Answers

0.09% increase.

Difference in price / original price

9.77 - 9.68 = 0.09
0.09/9.68 = 0.00929
Move two decimal points to the right = 0.9%

After four days, Trudy's average exercise time was 45 minutes per day. If she exercises 60 minutes on the fifth day, what will be her average time in

Answers

Answer:

240

Step-by-step explanation:

because adding the 45's 4 times then adding 60.

sorry if im wrong btw.

Math help 3 help me please!

Answers

#1

Answers are

Perpendicular bisector of KL

Only this rest are not possible

#2

No perpendicular bisectorAngle bisectorMedian Altitude

#3

Perpendicular bisectorAngle bisectorMedianAltitude

What is the exact value of 5 5/6 - (1 1/4 + 3 7/8)?

A. 17/24

B. 1 1/6

C. 8 11/24

D. 10 23/24

Answers

Answer: A) 17/24
Explanation:

Answer is linked below.

Answers

Answer:

- 7x² + 12x - 9

Step-by-step explanation:

Given:

A = 3x² - 7x + 8B = x² + 8x - 3C = - 5x² - 3x + 2

Find B + C - A:

B + C - A = x² + 8x - 3 + (- 5x² - 3x + 2) - (3x² - 7x + 8) = x² + 8x - 3 - 5x² - 3x + 2 - 3x² + 7x - 8 =(1 - 5 - 3)x² + (8 - 3 + 7)x + (-3 + 2 - 8) = - 7x² + 12x - 9

A = [tex]3x² - 7x + 8[/tex]

B = [tex]x² + 8x - 3[/tex]

C = [tex]-5x²-3x + 2[/tex]

Lets find B + C - A :

→ [tex]B + C - A[/tex]

→ [tex]x² + 8x - 3+ (- 5x²-3x + 2)-(3x² - 7x + 8)[/tex]

→ [tex]x² + 8x - 3-5x² - 3x + 2-3x² + 7x - 8[/tex]

→[tex] (1-5-3)x² + (8 -3 + 7)x+ (-3 + 2 - 8)[/tex]

→ [tex]- 7x² + 12x - 9[/tex]

Suppose that 12 inches of wire costs 48 cents.
At the same rate, how much (in cents) will 31 inches of wire cost?

Answers

Answer:

It will cost 124 cents to buy 31 inches of wire.

Step-by-step explanation:

12 inches costs 48 cents

1 inches will cost her [tex]\frac{48}{12}[/tex] → 4 cents

Then 31 inches will cost: 31 * 4 → 124 cents

Answer:

124 cents

Step-by-step explanation:

Solve using ratios since this is a proportional relationship:

12/48 = 31/x1/4 = 31/xx = 31*4x = 124 cents

Express each fraction as a percent. Round your answer to the nearest whole number. 76/125

Answers

Answer:

  61%

Step-by-step explanation:

Multiply the fraction by 100%.

  76/125 × 100% = (7600/125)% = 60.8% ≈ 61%

Substitute this simultaneous linear equation
[tex]x - 4y = - 6 \\ 2x + 3y = 10[/tex]

Answers

Answer:

[tex]x - 4y = - 6 \: ......(1) \\ \\ 2x + 3y = 10 \: .......(2)[/tex]

from equation (1)

[tex]x - 4y = - 6 \\ \\ 4y = x + 6 \\ \\ y = \frac{x + 6}{4} [/tex]

Substitute " y " in equation (2)

[tex]2x + 3y = 10 \\ \\ 2x + 3( \frac{x + 6}{4} ) = 10 \\ \\ 2x +( \frac{3x + 18}{4} ) = 10 \\ \\ \\ \frac{8x + 3x + 18}{4} = 10 \\ \\ \\ 8x + 3x + 18 = 10 \times 4 \\ \\ 11x + 18 = 40 \\ \\ 11x = 40 - 18 \\ 11x = 22 \\ \\ x = \frac{22}{11} \\ \\ x = 2[/tex]

[tex]y = \frac{x + 6}{4} \\ \\ y = \frac{2 + 6}{4} \\ \\ y = \frac{8}{4} \\ \\ y = 2[/tex]

The prime number in the following list is....
A. 19
B. 21
C. 38
D. 39​

Answers

Answer:

19

Step-by-step explanation:

Answer:

19

because it has only two factors and prime has only two factors

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