What is the value of sin cos theta?

Answers

Answer 1

If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2

We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.

And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.

Given that  sinθ⋅cosθ = 1/2

2(sinθ⋅cosθ) = 1             .........(1)

We know that trigonometric identity,

sin(2θ) = 2 sinθ cosθ

so equation (1) becomes,

sin(2θ) = 1            

We know that sin(π/2) = 1

Comparing with equation sin(2θ) = 1 we get,

2θ = π/2

θ = π/4          

Using trigonometric table,

sin(π/4) = 1/√2

and cos(π/4) = 1/√2

The value of  sinθ+cosθ would be,

sin(π/4) + cos(π/4)

= (1/√2) + (1/√2)

= 2/√2

= √2

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The complete question is:

If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ


Related Questions

Question 17
Galle bought a purse for $22.50. Gale's thend Brenda saw the purse and said she would give Gale $35 if Gale would sell her the new purse right then.
mely how much profit as a percent did Gale make from selling the purse to Brenda?
A.35.7%
B.55.6%
C.64.3%
D.155.6%

Answers

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

What is profit and loss?

Profit and Loss is a financial statement that shows a company's revenue, costs, and expenses over a certain period of time, such as a month or a year. The purpose of a P&L statement is to show the company's financial performance and to determine whether the company is making a profit or incurring a loss.

What is Profit Percentage?

The proportion that the retailer makes after selling a good at a price greater than its cost is the product's profit margin. P% indicates it.

Profit Percentage P% = {(selling price – cost price) / cost price} x 100.

The selling price of the purse is $35 and the original cost of the purse is $22.50. So the profit is $35 - $22.50 = $12.50

Profit as a percent = (Profit / Original cost) * 100

Profit as a percent = ($12.50 / $22.50) * 100 = 55.6%

So Gale made a profit of 55.6% by selling the purse to Brenda. Therefore the correct answer would be B. 55.6%

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PLEASE HELP
Explain what the unit rate means in the context of the problem.

Answer in at least two complete sentences.

Answers

Answer:

Step-by-step explanation:

A unit rate means a rate for one of something. You should write it as a ratio with a denominator of one.

For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate

IT's  0.80 per serving i think

A service station tracks the number of cars they service per day. Construct a histogram for the data and describe the shape of the distribution

Answers

Answer:

See attachment for histogram

The histogram is left skewed

Step-by-step explanation:

Given

[tex]40, 47, 37, 42, 46, 31, 50, 41, 17[/tex]

[tex]43, 46, 45, 21, 43, 45, 23, 49, 50[/tex]

[tex]48, 26, 42, 46, 35, 52, 27, 51, 31[/tex]

[tex]44, 35, 27, 46, 39, 33, 50, 45, 50[/tex]

Solving (a): Construct a histogram

First, we construct a frequency table

Calculate Range

[tex]Range = Highest - Least[/tex]

[tex]Range = 52 - 17[/tex]

[tex]Range = 35[/tex]

Using a class width of 5, we have the following classes:

[tex]17 - 22; 23 - 28; 29 - 34; 35 - 40; 41 - 46; 47 - 52[/tex]

So, the frequency table is:

[tex]\begin{array}{ccccccc}{Class} & {17-22} & {23-28} & {29-34} & {35-40} & {41-46} & {47-52} \ \\ {Count} & {2} & {4} & {3} & {5} & {13} & {9} \ \end{array}[/tex]

See attachment for histogram

From the attached histogram, we can see that the height of the bars of the histogram tend to increase towards the left.

Hence, the shape of the histogram is left skewed

Suppose that ƒ(−1)=10 and ƒ'(x)≥−3 for all values of x. What is the least possible value of ƒ(3)?

Answers

Using the mean value theorem, the least possible value of f(3) is - 2

What is the mean value theorem?

The mean value theorem states that for a function f(x) on the interval (a, b), there exists a value c such that

f'(c) = f(b) - f(a)/(b - a)

How to find the least possible value for f(3)?

Since ƒ(−1) = 10 and ƒ'(x) ≥−3 for all values of x, we require the least possible value of f(3).

Using the mean value theorem where

b = 3, a = -1 and f'(c) ≥ 3.

We choose f'(c) = 3 since f'(x) = 3 is the minimum value of f'(x).

So, substituting the values of the variables into the equation, we have that

f'(c) = f(b) - f(a)/(b - a)

f'(x) = f(3) - f(-1)/(3 - (-1))

f'(x) = f(3) - f(-1)/(3 + 1)

f'(x) = f(3) - f(-1)/4

So, making f(3) subject of the formula, we have that

f(3) = f(-1) + 4f'(x)

Since

f'(x) = 3 and f(-1) = 10,

Substituting the values of the variables into the equation, we have that

f(3) = f(-1) + 4f'(x)

f(3) = 10 + 4(-3)

f(3) = 10 - 12

f(3) = - 2

So, the least possible value is - 2

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HELP ME PLZ I NEED HELP

Answers

Answer:

A

Step-by-step explanation:

[tex]\frac{12}{a} = \frac{9}{b} => 12b = 9a[/tex]

[tex]12 * 1.5 = 9 * 2[/tex]

[tex]18 = 18[/tex]

This option works

Please help, I’m having trouble answering this question

Answers

Answer:

13+5+7+5+5

Its because if you calculate it mean and media. will be 7 and obviously mode is 5

Hope you're helped!

I don’t know this question
help me

Answers

The number of groups of like terms is 3

What is an algebraic expression?

An algebraic expression is defined as an expression made up of terms, variables, coefficients, constants, and factors.

These algebraic expressions are also composed of mathematical operations, such as;

AdditionSubtractionDivisionBracketParenthesesMultiplication, etc

A term can be described a single variable, number or numbers and variables that are multiplied together.

From the information given, we have the terms;

3x¹³, 9x¹⁰, -1x¹³, -16x¹³, 3x¹⁰, 3¹³, 10x¹⁰, 13x¹⁰

The similar terms are;

3x¹³,  3x¹⁰,  3¹³

Hence, the number is 3

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6 x/11 ➕1

What does x equal

Answers

X is 55 after rearranging the equation given

Suppose the diameter of a circle is 4units. What is its circumference?

Answers

Answer:

C = 12.6 (rounded to the nearest tenth)

Step-by-step explanation:

The formula for the circumference of a circle is C = 2πr

R = radius

The radius is the half of a diameter, so 4/2 is 2.

C = 2π(2)

C = 12.56637061

HELP ASAP, LINKS AND ABSURD ANSWERS WILL BE REPORTED! I WILL MARK BRAINLIEST!!

Answers

Answer:

3/4

Step-by-step explanation:

brainliest please

Answer:

(x so long as x is less than or equal to .7 and x is grater than 0.) I think, The number line is hard to interpret. if it's asking where the line stops then it is 7/10. but the answer in parentheses makes the most sense to me.

Step-by-step explanation:

                                                         Good Luck

                                                      Have a nice day

5. Emmanuel makes 82,000 as a software designer. Use the follow tax chart to find what he will pay in taxes this year.
A. 4925
B. 5456
C. 1245
D. 3426

Answers

I think the answer is d

NO WEBSITES/ fake links or your getting reported! Help me with ALL the problems!

Answers

1) we need to find the common denominator so we can multiply the denominators with each other.

[tex]\frac{6*4}{10*4}[/tex][tex]+\frac{3*10}{4*10}[/tex][tex]=\frac{24}{40} +\frac{30}{40}[/tex][tex]=\frac{54}{40}=1\frac{14}{40}[/tex]

2) make first fraction into improper fraction

[tex]\frac{20}{12} -\frac{2}{3} =\frac{20}{12} -\frac{2*4}{3*4} =\frac{20}{12} -\frac{8}{12}=\frac{12}{12} =1[/tex]

3) turn into improper fraction[tex]\frac{3}{4}+\frac{12}{5} +\frac{3}{4} =\frac{3*5}{4*5}+\frac{12*4}{5*4} +\frac{3*5}{4*5}=\frac{15}{20}+\frac{48}{20}+\frac{15}{20}=\frac{78}{20}[/tex]

4) turn into improper fraction

[tex]\frac{38}{8} +\frac{14}{5} =\frac{38*5}{8*5} +\frac{14*8}{5*8}=\frac{190}{40} + \frac{112}{40}=\frac{302}{40}[/tex]

then we minus 2 3/4

[tex]\frac{302}{40} - \frac{11}{4} = \frac{302}{40} - \frac{11*10}{4*10}=\frac{302}{40} - \frac{110}{40}=\frac{192}{40}[/tex]

5) 7/3= 2.33333333333 or [tex]2 \frac{1}{3}[/tex]

How do you check whether 7 3x is a factor of 3x3 7x?

Answers

7 + 3x is not a factor of expression 3x^3 + 7x

Consider given expression  3x^3 + 7x

Let f(x) = 3x^3 + 7x

Assume that  7 + 3x is a factor of 3x^3 + 7x

This means,  7 + 3x = 0 would be the root.

x = -7/3

If x = -7/3 is root of polynomial f(x) = 3x^3 + 7x then f(-7/3) must be equal to 0

We find the value of given polynomial for x = -7/3

f(x) = 3x^3 + 7x

f(-7/3) = 3(-7 / 3)^3 + 7 (-7 / 3)

f(-7/3) = (3 × (-343)) / 27 + (-49 / 3)

f(-7/3) =  [(-343) - 147] / 9

f(-7/3) = -490 / 9

f(-7/3) ≠ 0

Since f(-7/3) ≠ 0, x = -7/3 is not root of polynomial  f(x) = 3x^3 + 7x

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Find the volume of this

Answers

Answer:

37.8 yd^3

Step-by-step explanation:

base area = (4.5 x 2.8)/2 = 6.3 yd^2

Volume = 6.3 x 6 = 37.8 yd^3

please help you will get brainliest!

Answers

Question 13 is 66
Question 8 is 104

The link above is a scam don’t open it

the perimeter of a right triangle is 24 ft, and one of its legs measures 6 ft. Find the length of the other leg and the hypotenuse.
a) 6 ft, 12ft
b) 5 ft, 13 ft
c) 8 ft, 10 ft
d) 7 ft, 11 ft

Answers

Answer:

Step-by-step explanation:

We know the perimeter of a triangle is the sum of all the sides( two legs and one hypotenuse).

By pythagoras we know that

[tex]h^2= a^2+b^2.[/tex]

and the perimeter is [tex]P=h+a+b[/tex].

Since P=24 and a=6  we have these equations:

[tex]h^2=36+b^2\\24=h+6+b[/tex]

From the last equation we have [tex]h=18-b[/tex]. Replace h in the first equation we get that

[tex](18-b)^2=36+b^2[/tex]

[tex]18^2-36b+b^2=36+b^2\\288=36b\\b=\frac{288}{36}=8[/tex]

and h=18-8=10

9. Calculate the volume of the sphere
8 cm
A. 2144 66 cm
B. 64 cm
C. 200.96 cm
D. 448.12 cm

Answers

(4/3)×(22/7)×(8cm^3)

32% of the students in the class forgot to charge their computer. If there are 25 total
students in the class, how many forgot to charge their computer?

Answers

8 students forgot to charger their computers

A meteor crashed onto a planet and caused a crater that was 15,219.88 in deep. Round your answer to the nearest tenth.​

Answers

Answer:

15,219.90

Step-by-step explanation:

.88 rounded to the nearest tenth would be 90. 8 is closer to 10 than 0 therfore you round up to .90

The vertices of a convex pentagon are $(-1, -1), (-3, 4), (1, 7), (6, 5)$ and $(3, -1)$. What is the area of the pentagon

Answers

On solving the provided question, we can say that vertices of pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1); Area = 30 sq unit

what is a pentagon?

A pentagon is a polygon with five sides that is used in geometry. The inner angles of a straightforward pentagon add up to 540°. Simple or self-intersecting pentagons are both possible. A pentagram is a self-intersecting regular pentagon. Five angles and all sides of a regular pentagon are equal. It is referred to as an irregular pentagon if the side lengths and angle measurements do not match. All outside angles, as far as we are aware, balance out inside angles. The polygon's exterior angle total is therefore equal to n(360°/n). There are five sides to a pentagon, therefore n must equal five. Consequently, 5(360°/5) = 360° is the sum of the pentagon's outer angles.

vertices of a convex pentagon are (-1, -1), (-3, 4), (1, 7), (6, 5) and (3, -1).

Area = 1/2 [ 24+3+15+0-3] - [3-30-3+9-0]

Area = 1/2| 60 |

Area of pentagon  = 30 sq unit

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a question that can be answered by collecting data that will vary. "On average, how old are the people who live in my building?" is an example.

A. Mean
B. Mode
C. statistical question

Answers

I believe that is C. Statistical question.

I know it’s not B because that has nothing so do with the question so you’re good there. While A could be a potential answer, it says a question that can be answered by collecting data, whereas the mean would actually be that data and not the question that can be answered so C would be the only choice left.

What is the solution of 2x² 3x 2 0?

Answers

The equation 2x² + 3x - 2 = 0 has the solutions or roots 1 and -2. The quadratic equation is 2x² + 3x - 2 = 0

what is equation ?

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter.

given

Below is the quadratic equation.

2x² + 3x - 2 = 0

When you factor the equation, you get

2x² + 3x - 2 = 0

2x² + 4x - x - 2 = 0

2x(x + 2) - 1(x + 2) = 0

(x - 1)(x + 2)

x = 1, -2

The equation 2x2 + 3x - 2 = 0 has the solutions or roots 1 and -2

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The list shows the score of each game completed at a bowling alley during a one-hour period.
90, 96, 120, 124, 130, 135, 138, 140, 145, 148, 290, 290
How would the data graphed on a horizontal number line appear to be clustered or skewed? Explain your answer,

Answers

Answer:

it would be clustered because the scores are all close together :)

It would be clustered because the scores are all close together.

We have given that,

The list shows the score of each game completed at a bowling alley during a one-hour period.

90, 96, 120, 124, 130, 135, 138, 140, 145, 148, 290, 290.

What is clustered or skewed?

Grouping similar objects into common groups, also known as clustering, is an important problem of unsupervised machine learning.

We have to determine the data graphed on a horizontal number line appear to be clustered or skewed.

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click the image for the question someone pls help i suck at algebra ill love u forever <3‼️

Answers

Answer:

$ 30,000

Step-by-step explanation:

c = 300 ³√n²

= 300× ³√1000²

= 300× 100

= 30,000

Answer: $30000

Step-by-step explanation:

[tex]300\sqrt[3]{n^2}[/tex]

[tex]300\sqrt[3]{1000^2}[/tex]

[tex]300\sqrt[3]{1000000}[/tex]

300 × 100 = 30000

Whats is two fifths divided by one sixth

Answers

Easy ur answer is 2.4!!!!

Answer:

2 2/5

Step-by-step explanation:

For each set of values for a and b evaluate the given expressions and record your answers in the table. ( I only need this one).


A = -1/2 B =6

A divided by -b

PLEASE HELP

Answers

Answer:

Set1 = 1/12

Set2 = 1/12

Set3 = -12

Step-by-step explanation:

Substitute, use Keep-Change-Flip to handle division when there's fractions involved. See image.

Also to multiply fractions, multiply

top×top and bottom×bottom straight across. Also negative times a negative is a positive and negative is like opposite so -(-6) is 6 and -(-1/2) is 1/2.

see image.

—PLEASE HELP QUESTION IS IN PIC—

Answers

Answer:

ur answer is A

Step-by-step explanation:

I just did the problem

Find the difference quotient of the exponential function, f(x) = e^x

Answers

Answer:

Step-by-step explanation:

The difference quotient in general looks like

[tex]\frac{f(x+h)-f(x)}{h}[/tex]   Sometimes the symbol "delta x"  [tex]\Delta x[/tex]   is used instead of h.

For the exponential function, the difference quotient is

[tex]\frac{e^{x+h}-e^x}{h}[/tex]

Answer:

For those who dont want to read, its A.

Step-by-step explanation:

Edge 2021

Can someone help me with this? I've asked my teachers and I'm still lost

Answers

Answer:

Click the link?

Step-by-step explanation:

Answer:

so well go to the guide and check the q. Then either create an doc or slide when done click file then download then pdf. k. then click add file then add the pdf file.

Step-by-step explanation:

Find the area of a circle with a diameter of 16 meters. Round your answer to the nearest hundredth of a square meter.

Answers

Answer:

201.00

Step-by-step explanation:

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