Why is the sine of an acute angle less than one?

Answers

Answer 1

The sine of an acute angle is less than one because it is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. Since the side opposite the angle is shorter than the hypotenuse, the ratio is always less than one.

To what does sin equate?

In contrast to the cosine of an angle, which corresponds to the ratio of the nearby side to the hypotenuse, the sine of an angle is the ratio of the opposite side to the hypotenuse.

It's also the same reason why the cosine of an acute angle is always less than one because it is the ratio of the adjacent side of the angle to the hypotenuse.

It's important to note that this is only true for acute angles, angles smaller than 90 degrees.

For obtuse angles, greater than 90 degrees, the sine and cosine values are greater than one.

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Related Questions

Caculate the total amount from a simple interest account
Principal $300
interest rate 7%
Time 2

Answers

Answer:

$42.00

Step-by-step explanation:

Interest = principle x rate x time

Interest = 300 x .07 x 2

Interest = 42

Clara baked a sheet cake with a length of 0.5 meters. She covered the cake in small 1 frosting polka dots that are the length of the cake. What is the approximate 100 length of a polka dot, in meters?​

Answers

Answer:

kkuguftfhbnkmom ugvtvtv uvbuub

Frank earns an annual salary of $42,800. He pays 8% in total taxes. How much money will Frank pay in taxes each year?

Answers

Answer:

$3424

Step-by-step explanation:

42800 x .08

.08 = 8%

60 workers can complete a work in 21 days. How long will it take to complete the some work if 10 more workers were added?​

Answers

Answer:

Step-by-step explanation:

set 1 is the work, then 60 works finish 1/21 per day. [tex]\frac{1}{21*60}[/tex] is the work for per workers. so, the days for 70 workers is [tex]\frac{21*60}{70}=18[/tex] days.

it will spend 18 days to complete

A solution set always includes...

A. all the numbers that make the inequality false.

B. all the numbers that make the inequality true.

C. zero and infinity.

D. negative infinity.

Answers

I think the answer is going to be a

Answer:

A

Step-by-step explanation:

i got the same answer and got ir right

Mrs. Harris took 6 oranges out of the refrigerator and cut them into wedges, each wedge represents 1/6 of the entire orange. Her children at 3/4 of the wedges.

A) how many wedges did her children eat

B) how many wedges are left?

Answers

A = 27
B = 9

Total orange = 6
One orange wedge = 6
Total wedge = 6*6 = 36
36 / 4 = 9
9*3 = 27
36-27 = 9
If it is helpful t

Which point represents the approximate location of 388 squared

Answers

Answer:

Point D

[tex] \sqrt{388} = 19.7 \\ between \: 19 \: and \: 20[/tex]

The picture shows a shed. Find the length, AB, of the roof.​

Answers

The length AB of the roof is 3.20 m.

What is the Pythagorean theorem.

The Pythagorean theorem is one that can be used to determine the value of the unknown side of a right triangle when given two of its sides.

The theorem states that;

/Hyp/^2 = /Adj/^2 + /Opp/^2

Considering the given picture of the shed, draw a perpendicular to B from a point C on parallel line A. So that the length of AB can be referred to as the hypotenuse of triangle ABC.

Now applying the Pythagorean theorem, we have;

/Hyp/^2 = /Adj/^2 + /Opp/^2

/AB/^2 = /2/^2 + /2.5/^2

            = 4 + 6.25

/AB/^2 = 10.25

AB = (10.25)^ 1/2

AB = 3.20

Thus, the length of AB of the roof is 3.20 m.

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Jamila deposits $800 in an account that earns yearly simple interest at a rate of 2.65%. How much money is in the account after 3 years and 9 months?

Answers

Answer:

$821.2

Step-by-step explanation:

cause 2.65 percentage of 800 dollars is 800/100=8*2.65=21.2dollars.+800 =$821.2

Please help! Will give brainiest to correct person!! No links please!

Answers

Answer:

39 inch

Step-by-step explanation:

Answer:

H=39.0625

Step-by-step explanation:

D=32in

R=1/2d=32/2=16

Volume of cylinder:pi r^2h

V=pir^2h

10000pi=16^2hpi

256h=10000

h=39.0625

A bag of

.5 red marbles

.6 blue marbles

.3 green marbles

.4 black marbles

.2 yellow marbles

A marble will be drawn from the bag and replaced 100 times how many green and black marbles will be drawn?

Answers

The number of green and black marbles will be 15 and 20 black marbles respectively.

How to illustrate the probability?

Probability simply means the chance that a particular thing or event will happen. It is the occurence of likely events. It is simply the area of mathematics that deals with the numerical estimates of the chance that an event will occur or that a particular statement is true.

We have the following information:

5 red marbles

6 blue marbles

3 green marbles

4 black marbles

2 yellow marbles

Total marble = 20 marbles

The number of green marbles:

= 3/20 × 100

= 15

The black marbles will be:

= 4/20 × 100

= 20

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What are the 3 steps for solving a quadratic equation?

Answers

Determine what a, b, and c are worth. the quadratic formula in writing. After that, enter the values for a, b, and c. Simplify.

what is quadratic equation ?

A quadratic polynomial in a single variable is represented by the expression x ax2+bx+c=0, which is a quadratic equation. a 0. Since it is a second order polynomial, the Fundamental Theorem of Algebra guarantees that it has at least one solution. Simple or difficult solutions are both possible. The term "quadratic equation" refers to an equation that is quadratic. It must square at least one word, according to this indication. One of the common solutions for quadratic equations is the formula "ax2 + bx + c = 0." where the variables "X" are undefined and are numerical coefficients or constants a, b, and c.

given

steps are

Find out what a, b, and c are worth.

Quadratic formula: write it down.

Add the values of a, b, and c after that. Simplify.

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An ice cream factory makes 310 quarts of ice cream in 10 hours how many quarts could be made in 48 hours what was the ate per day

Answers

The factory can make 744 quarts of ice cream per day.

To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:

310 quarts / 10 hours = x quarts / 48 hours

To solve for x, we can cross multiply:

310 quarts * 48 hours = 10 hours * x quarts

x = (310 quarts * 48 hours) / 10 hours = 1480 quarts

So the factory could make 1480 quarts of ice cream in 48 hours.

To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:

rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day

So the factory can make 744 quarts of ice cream per day.

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Jelani has twice as much money on his subway pass as Alexis. If they both add $20 to their passes, Jelani will have 1.5 times as much on his pass as Alexis. Write an equation to represent this situation. How much do Jelani and Alexis have on their subway passes now?

Answers

Answer:

x = 2x

x + 20 = 2x + 20

And,

1.5(x + 20) = 2x + 20

x = 20 i.e. Alexis

And, Jelani be 40

Step-by-step explanation:

Given that

Jelani has twice as much as Alexis

And, both can added $20

Jelani will have 1.5 times as much on his pass on Alexis

We need to write an equation also the amount does Jelani and Alexis have

So,

Let us assume the alexis be x

And, Jelani be 2x

Now

x = 2x

x + 20 = 2x + 20

And,

1.5(x + 20) = 2x + 20

1.5x + 30 = 2x + 20

-0.5x = -10

x = 20 i.e. Alexis

And, Jelani be 40


Marshall has $8.25 totally in his collection, consisting of quarters and nickels. The number of nickels is three more than the number of quarters. How many nickels and how
many quarters does Ross have?

Answers

Answer:

where did Ross come from? is that just misplaced or what. or am I reading it all wrong

Solve the following equation for mathwatch
3x-1/2= x+5/5

Answers

0.75 i think

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=34x=34

Decimal Form:

0.75

t(28 – 8) = 24(28 – 8)
- 24 1)

Answers

Answer:

24(24)

Step-by-step explanation:

[tex] \rm \mapsto \: t(28 - 8) = 24(28 - 8) \\ \rm \mapsto \: t(24) = 24(24) \\ \rm \mapsto \: 24t = 576 \\ \rm \mapsto \: t = \frac{576}{24} \\ \rm \mapsto \: t = 24[/tex]

The solution to the equations are

a) The quantity ( 28 - 8 ) represents the discounted price of the tickets

b) The total cost of the 24 tickets is given by the equation A = $ 480

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of 24 tickets be represented as A

Now , the equation will be

The initial cost of a ticket = $ 28

The discounted cost of the ticket = $ 8

So , the final cost of the ticket = $ 28 - $ 8 = $ 20

Now , the cost of t tickets = 20t

So , when the value of t = 24

Substitute the value of t in the equation , we get

The cost of 24 tickets A = 20 ( 24 )

On simplifying the equation , we get

The cost of 24 tickets A = $ 480

Therefore , the value of A is $ 480

Hence , the equation is A = $ 480

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Sara had 222 dollars to spend on 9 books after buying then she had 15 dollars how much did each book cost

Answers

23 dollar for each book

Answer:

each book cost=222-15=207/9=22.88 dollar

How do you multiply FG?

Answers

FG cannot be multiplied because it is not a numerical value.

Multiplication is a mathematical operation that involves multiplying two numerical values together to produce a single numerical result. In order for multiplication to be possible, both values must be numerical values. FG is not a numerical value, which means that it cannot be multiplied. In order for FG to be multiplied, it would need to be replaced with a numerical value, such as a number or an expression that can be evaluated to a number. Without a numerical value, multiplication is not possible. Multiplying numerical values is done by taking the product of the two values, meaning that the result of the multiplication is the sum of each value multiplied by itself the number of times the other value is. For example, if you were to multiply 3 and 4, the result would be 12 because 3 multiplied by itself 4 times is 12, and 4 multiplied by itself 3 times is also 12. Without numerical values, this operation cannot be performed.

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Substitution method.
y=x - 5
y —3х – у = -3

Answers

Answer : ( 1, - 4 )

Explanation : y=x - 5

y —3х – у = -3

Step 1 : Consider the first eqaution. Subtract X from both sides.

y - x = -5

Step 2 : Consider the second eqaution. Combine y and -y to get 0 .

-3x = -3

Step 3 : Divide both sides by -3

x = -3 / -3

Step 4 : Divide -3 by -3 to get 1

x = 1

Step 5 : Consider the first eqaution. Insert the known values of variables into the equation.

y - 1 = -5

Step 6 : Add one to both sides.

y = -5 + 1

Step 7 : Add negative 5 and one to get negative 4 .

y = -4

Therefore, the answer is ( 1, - 4 )

What is the domain and range of √ X 2?

Answers

The domain of √ X  2 is X ≥ 4. The range is all real numbers.

Here is the proof, In order for the square root to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. In this case, the radicand is X - 2, so we must have X - 2 ≥ 0, which is equivalent to X ≥ 4. Therefore, the domain of √ X - 2 is all values of X that are greater than or equal to 4. The range of √ X - 2 is all real numbers because the square root of any non-negative value is a real number.

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Rewrite 7[tex]x^{\frac{1}{2}[/tex] as a radical expression

Answers

basically, the denominator will always be the number outside of the radical and the numerator will always be your exponent. If it’s one, you don’t put it in because if there is no exponent, it’s an invisible one
The answer would be 7 square root x

* I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER*
A circle has a circumference of 10 millimeters. What is the circle's diameter? Use 3.14 for pi and round your answer to the nearest tenth.

Answers

Answer:

To find the diameter divide the circumference by pi

10÷3.14

=3.2 mm

Answer: C3.2

Explanation

I need to know the andwer to 0.03 divided by 0.81 in division of decimals

Answers

Answer: 0.0370 (Italic part repeats forever)

Step-by-step explanation:

Answer: 0.037...

Step-by-step explanation:

Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.

Answers

Answer:

C) {6+√43, 6-√43}

Step-by-step explanation:

Applying,

x = [-b±√(b²-4ac)]/2a.................... Equation 1

From the question,

Given: a = 1, b = -12, c = 7

Substitute these values into equation 1

x = [-(-12)±√(-12²+4×1×7)]/2×1

x = [12±√(144+28)]/2

x = [12±√172]/2

either,

x = (12-√172)/2

x = (12-2√43)2

x = (6+√43)

or

x = (12+√172)/2

x = (12+2√43)/2

x = (6+√43)

Hence,

The right answer is C). {6+√43, 6-√43}

Martin will earn $20 per hour at a new job. During training, he will earn $15 per hour. What percent of Martin’s regular hourly rate will he earn during training?

Answers

Answer:

5

Step-by-step explanation:

temperature of an oven in a laboratory rises until it reaches a maximum temperature of 32°C. The oven then stops heating and reactivates only when the temperature goes down to a minimum of 18°C. At 12:00 pm, the oven starts at room temperature, which is 18°C, and takes 3 hours to reach 32°C Write a function in the form 0(t)= Acos(bt)+c, that represents the temperature of the oven, O. in terms of the number of hours, t, since 12:00pm. Then, sketch the function on the provided grid for one full cycle. Be sure to scale your axes trig.

Answers

Answer:

123456789123345

Step-by-step explanation:

need help with this

Answers

It’s an acute angle but need help with what?

Answer:

im sorry what exsactly is the question?

Step-by-step explanation:

Monty is working on a formula to determine the amount of profit (P) he will make when he sells his pottery. He has already spent $50 on materials and plans to sell each pot for $5. If x represents the number of pots he sells, which formula represents Monty's profit from his sales?

Answers

Answer:

P=5x-50

Step-by-step explanation:

Profit is represented by P.

$5 is what Monty plans to sell each pot for and x represents how many pots he sells.

therefore 5x-50=P

Molly bought a large basket of 60 apples.

When she got home, she found 4 rotten

ones. If she goes back and buys 200 more

apples, how many rotten apples would she

expect there to be?

Group of answer choices

20

24

13

8

Answers

Step-by-step explanation:

1. 60 apples

2. 60-4=56

3. 56+200=256

200/60

60/4

60+60=120

120+60=180

I think either 13.

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