Answer:
An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians). It is the inverse function of the basic trigonometric functions.
Step-by-step explanation:
Trigonometric functions are derived from ratios of certain sides of a right triangle in reference to an angle. The graph of which is a wave, with amplitude in the y-axis and angle in the x-axis. We will first define the sine function written as:
sin(θ)=oppositesidehypotenuse
As we can see, the sine function, together with all the other trigonometric functions, relates an angle to the ratio of an opposite side and the hypotenuse of right triangle. The input here is an angle, and the output is a ratio. Therefore, the inverse process to this is actually just a reverse process.
Let
y
=
s
i
n
(
θ
)
y=sin(θ)
Then inverse trigonometric function outputs an angle. However, we can set y to its original value via transitivity:
s
i
n
−
1
(
y
)
=
θ
s
i
n
−
1
(
o
p
p
o
s
i
t
e
s
i
d
e
h
y
p
o
t
e
n
u
s
e
)
=
θ
sin−1(y)=θsin−1(oppositesidehypotenuse)=θ
Thus we see, that the input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
The input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
We need to find what is the input for inverse trigonometric functions.
What is the input for an inverse trigonometric function?An inverse trigonometric function is a function in which you can input a number and get/output an angle (usually in radians).
The inverse trigonometric functions do the same thing as the inverse trigonometric relations, but when an inverse function is used, because of its restricted range, it only gives one output per input--whichever angle lies within its range.
Example:
Inverse sine of 1/2 is the angle of 30°
That is, [tex]sin^{-1}(\frac{1}{2} )=30^o[/tex]
As we can see, the sine function, together with all the other trigonometric functions, relates an angle to the ratio of an opposite side and the hypotenuse of the right triangle. The input here is an angle, and the output is a ratio. Therefore, the inverse process to this is actually just a reverse process.
Therefore, the input to an inverse trigonometric function is a unitless ratio of two sides of a representative right triangle.
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Given that the measure of ∠x is 30°, and the measure of ∠y is 60°, find the measure of ∠z.
Answer:
90°
Step-by-step explanation:
Since vertical angles are equal, ∠x is equal to its vertical angle. Since the total angles in a triangle are 180, and x + y = 90, then the angle supplementary to z = 180 - 90 = 90. To find z, it's just 180 - 90 = 90.
The radius of a circle is 3 km. what is the circle's area and what is the formula you have to use?
Answer:
Circle's area = 28,26 km
Formula = π r²
Step-by-step explanation:
[tex]circle's \: \: area = \pi \: {r}^{2} \\ circle's \: \: area = 3,14 \times {3}^{2} \\ circle's \: \: area = 28,26 \: km \\ circle's \: \: area = 28.260 \: m[/tex]
27,965 is divisible by
A) 2
B) 3
C) 5
D) 8
Answer:
C) 5
Step-by-step explanation:
27,965/5 = 5593
Technically 27,965 can be divisible by any of these numbers but 5 i the only one that equals a whole number.
oliver turned a circular dial one degree if he turns the dial one degree 27 times, what is the measurement on the angle in degrees
Answer:
27 degrees.
Step-by-step explanation:
Please kindly check the attached file
If x = -5 and y = 3 x − 5, then y equals what number?
Answer:
-20
Step-by-step explanation:
Plug in -5 for x
Y=3(-5) -5
Y=-20
Hope this helped
:)
Answer:
-20
Step-by-step explanation:
y= 3x-5
y=3(-5)-5
y= -15-5
y= -20
n a newspaper, it was reported that yearly robberies in Springfield were down 20% to 176 in 2011 from 2010. How many robberies were there in Springfield in 2010?
Answer: There were 220 robberies in Springfield in 2010
Step-by-step explanation: If the robberies were reported to be down 20% and the new figure is 176, it simply means the figure 176 depicts 80% (or 0.8) of the figure from year 2010.
We shall take the figure in year 2010 as x, which is 100% (or 1.0) and year 2011 is 176 which is 80% (or 0.8). What we now have is;
176/x = 0.8
176/x = 4/5
By cross multiplication we now have;
(176 x 5)/4 = x
880/4 = x
220 = x
Therefore, there were 220 robberies in Springfield in 2010
Answer: There were 220 robberies in Springfield in 2010.
Step-by-step explanation:
Hi, to answer this question we have to write an equation with the information given.
Since the robberies decreased 20%, it means that 2011 are robberies are the 80% (100%-20%) of the 2010 robberies (x).
So if we multiply the yearly robberies in 2010 (x) by 0.8 (decimal form, 80/100=0.8) , we obtain the number of yearly robberies in 2011 (176).
x (0.80) = 176
Solving for x
x = 176/0.8
x = 220 robberies (2010)
Find the difference.
(4m^2 - m+2) - (-3m^2+ 10m + 4) =(
7m^2 - 11m - 2
Step-by-step explanation:Distribute the negative.
4m^2 - m + 2 + 3m^2 - 10m - 4 = ?
Now, add the like terms.
4m^2 + 3m^2 = 7m^2
-m + (-10m) = -11m
2 + (-4) = -2
7m^2 - 11m - 2
The expression 20,000(1.05)' represents the population of a town t years after 2005
Select the value from each drop-down menu that best completes the sentence.
The population of the town
by
• each year
Answer:
Step-by-step explanation:
The given expression represents exponential growth. The expression is written as
20,000(1.05)^t
Where
20000 represents the initial population of the town in 2005.
1.05 represents the rate at which the population is increasing each year after 2005. The actual growth rate is
0.05 × 100 = 5%
t represents the number of years after 2005
Therefore, the complete sentence would be
The population of the town is increasing by 5% each year.
What is the radius of a hemisphere with a volume of 49037 ft", to the nearest tenth
of a foot?
Answer:
28.6 ft
Step-by-step explanation:
Given an hemisphere of volume [tex]49037 ft^3[/tex]
Volume of a Hemisphere of radius r [tex]=\frac{2}{3}\pi r^3[/tex]
Therefore:
[tex]\frac{2}{3}\pi r^3=49037 \\r^3=49037 X \frac{3}{2 \pi}\\r=\sqrt[3]{49037 X \frac{3}{2 \pi}} \\r=28.6\: foot[/tex]
The radius of the hemisphere is 28.6 foot to the nearest tenth.
Use any method to solve the equation. If necessary, round to the nearest hundredth. 9x^2 = 17
Answer:
1.37
Step-by-step explanation:
First, we want to isolate the variable x. Do this by dividing both sides by 9:
[tex]\frac{9x^2}{9} =17/9[/tex]
[tex]x^{2} =17/9[/tex]
Now, square root both sides:
[tex]\sqrt{x^2}= \sqrt{17/9}[/tex]
x = [tex]\sqrt{17/9} =\sqrt{17}/3[/tex]
Finally, we can use a calculator to finish off the problem:
x = [tex]\sqrt{17}/3[/tex] ≈ 1.37
Hope this helps!
9x^2 = 17
Divide both sides by 9
X^2 = 17/9
Take the square root of both sides
X = sqrt(17/9) and -sqrt(17/9)
Simplify:
X = sqrt(17)/3 and -sqrt(17)/3
Find the volume of the composite figure to the nearest whole number. The cylinder in the middle of the prism is hollow and should not be included in the volume.
The nearest whole number, the volume of the composite figure is 1140 in^3.
The composite figure consists of two rectangular prisms. The first prism has dimensions 8 in. x 4 in. x 18 in., and the second prism has dimensions 10 in. x 4 in. x 18 in.
To find the volume of the composite figure, we need to subtract the volume of the hollow cylinder from the volume of the two rectangular prisms.
The volume of a rectangular prism is calculated as follows:
Volume = length x width x height
The volume of the first rectangular prism is therefore:
Volume = 8 in. x 4 in. x 18 in. = 576 in^3
The volume of the second rectangular prism is therefore:
Volume = 10 in. x 4 in. x 18 in. = 720 in^3
The volume of a cylinder is calculated as follows:
Volume = π * radius^2 * height
Since the cylinder in the middle of the prism is hollow, we only need to consider the volume of the cylinder wall. The radius of the cylinder is 1 in., and the height of the cylinder is 18 in. Therefore, the volume of the cylinder wall is:
Volume = π * 1 in.^2 * 18 in. = 56.52 in^3
The total volume of the composite figure is therefore:
Volume = (576 in^3 + 720 in^3) - 56.52 in^3 = 1140.48 in^3
To the nearest whole number, the volume of the composite figure is 1140 in^3.
I need help with this I don’t understand this
Answer:
the answer would be A
Step-by-step explanation:
multiply 7 x 6 and that would get you to 42 and if you multiply 42 x 6 that would get you 252 and if you do that with the rest of the numbers you will see that it could work if you multiply them by 6 so basically the constant rate of the numbers would be 6.
Which equation has no solution?
O
4(x + 3) + 2x = 6(x + 2)
5+2(3 + 2x) = x + 3(x + 1)
5(x + 3) + x = 4(x + 3) + 3
4 + 6(2 + x) = 2(3x + 8)
O
Answer:
5 + 2(3 + 2x) = x + 3(x + 1)
Cindy asked to borrow Melinda's math book. Which sentence shows a correctly written response to Cindy's question?
Answer:
C
Step-by-step explanation:
For breakfast Jamie can choose from cereal, eggs, or a muffin. She also can drink coffee, orange juice, or milk. How many total outcomes are possible?
Jamie has 9 possible combinations for breakfast based on her choices of 3 different foods and 3 different drinks.
Explanation:The subject of the question is in the field of probability in mathematics. The question is asking for the total number of outcomes or combinations possible given Jamie's breakfast choices. Jamie can choose from 3 foods (cereal, eggs, muffin) and 3 drinks (coffee, orange juice, milk).
To find the total number of outcomes, you multiply the total number of options in each category. In this case, it would be 3 (food choices) multiplied by 3 (drink choices), which sets the total possible outcomes to be 9.
Therefore, Jamie has 9 possible combinations for her breakfast choice.
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What is the endpoint formula given midpoint?
Answer:
B = 2M -A
Step-by-step explanation:
For given endpoint A and midpoint M, the other endpoint B can be found using the definition of the midpoint:
M = (A+B)/2
2M = A+B . . . . . multiply by 2
2M-A = B . . . . . subtract A
The second endpoint can be found by subtracting the given endpoint from twice the midpoint:
B = 2M -A
I REALLY NEED HELP PLS ANSWER!!!!!
A rectangle sandbox has an area of 64 square yards. What might be the perimeter of the sandbox?
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
What’s the square root of 6
Answer:
2.44948974
Hope I could help.
Brainliest plz ;)
To make a glass sphere, 3,052.08 cm3 of molten glass is poured into a mold. Using 3.14 for π, Eduardo finds the circumference of the sphere using the steps below.
Which statement about Eduardo’s calculations is true?
Eduardo did not use the correct formula for the circumference.
Eduardo incorrectly used the length of the diameter to find the circumference.
Eduardo incorrectly calculated the radius.
Eduardo did not square the radius correctly in the second formula.
Answer:
Eduardo did not use the correct formula for the circumference.
Step-by-step explanation:
I was on the same question as you and guessed the assignment said this was the correct answer.
6x+10>5x-12
Help needed
Answer:
x > -22
Step-by-step explanation:
6x+10>5x-12
Subtract 5x from each side
6x-5x+10>5x-5x-12
x+10 > -12
Subtract 10 from each side
x+10-10>-12-10
x > -22
Giovanna owns a farm. She is going to randomly select one animal to present at the state fair. She has 6 pigs, 7 chickens, and 10 cows. What is P (chicken)
Answer:
P(chicken) ≈ 0.3
Step-by-step explanation:
Giovanna will select one animal from 6 pigs or 7 chickens or 10 cows to present at the state fair. From the question, there are a total of 6 + 7 + 10 = 23 animals to choose from.
If she selects a chicken, then P(chicken) = 7/23 = 0.304
P(chicken) ≈ 0.3
Answer:
7/23 OR 0.304...826
Step-by-step explanation:
Please refer to the attached image for explanations
Plzzz help thank you!!
Answer:
i think is 240 or it could be 64
Saige's spaceship traveled 588588588 kilometers (\text{km})(km)left parenthesis, start text, k, m, end text, right parenthesis in 606060 seconds (\text{s})(s)left parenthesis, start text, s, end text, right parenthesis.
Answer:
A is proportional
B and C are NOT proportional
Step-by-step explanation:
First, simplify 588 and 60:
588 divided by 6
60 divided by 6
= 98
10
Simplify them again by dividing them both by 2
= 49
5
Let's look at A:
441 and 45
Simplify by dividing by 9
= 49
5
It's pretty obvious that A is proportional because the simplified values are exactly the same.
Next, let's check B:
215 and 25
Simplify by dividing by 5
= 43
5
Now that its simplified you can compare
43 is smaller than 49
5 5
B is not proportional
Finally, let's check C:
649 and 110
Simplify by dividing by 11
= 51
10
Make 51 and 49 have the same denominator so we can compare them
10 5
51 can stay the same because 5 times 2 equals 10
10
49 times 2
5 times 2
= 98
10
Now that the denominators are the same we can compare
51 is much smaller than 98
10 10
Therefore, C is also not proportional.
Hope that helps :D
The velocity of Saige's spaceship is 9,809,809 km/s.
Explanation:Given that Saige's spaceship traveled 588,588,588 kilometers in 60 seconds, we can calculate the velocity of the spaceship by dividing the distance traveled by the time taken. Velocity = Distance / Time. Velocity = 588,588,588 km / 60 s = 9,809,809 km/s. Therefore, the velocity of Saige's spaceship is 9,809,809 km/s.
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Please help me Factor x2 − 4x + 5
Step-by-step explanation:
Look it's so simple once you learn it's very easy you have to multiply the 1 and 3rd digit so answer is 5 now you have to find the factors of 5 so
x2 - 4x + 5
x2 - 5x + x + 5
x (x - 5) +1 (x + 5)
(x - 5) (x + 1) are the factors but please recheck the question maybe there is a mistake in sign because my factors x + 5 and x - 5 this should be one sign either positive or negative
Which equation represents the relationship of the measure of m∠X and m∠Y?
Answer:
The measure of f m∠X and m∠Y =180 i.e they are supplementary angles.
Step-by-step explanation:
Given:
Two angles
To Find:
Relationship between them
Solution:
For two angles to have relationship ,we need to know what represents in the figure
Here no terms are used to represent the angles
So two angles can be represented in sum of angles of triangles ,
as Consider a triangle XYZ then
X +Y=180 -Z
This will be representation
Otherwise,
Then could be linear ,interior alternate angle or supplementary angles
Which they adds up to 180 degree.
Depending upon the Condition representation will be establish.
Now,
m∠X and m∠Y=180............Supplementary angles. will be most effective .
Answer:
m∠X + m∠Y = 180°
Step-by-step explanation:
Please answer this correctly
Answer:
approximately 18 or [tex]\sqrt{324}[/tex]
Step-by-step explanation:
please give me brainliest
A square has an area of 16 square millimeters. What is the length of each side of the square?
Answer:
The length of each side of the square is 4 mm
Step-by-step explanation:
AS we can see that , it is said that it is as square so all sides of a square are equal
Area(A)= 16 square millimetres
Length (L) = ?
or
[tex]L^{2}[/tex] = Area
[tex]L^{2}[/tex] = 16
L = [tex]\sqrt{16}[/tex]
L =[tex]\sqrt 4^{2}[/tex]
Therefore L = 4 mm
Hope it will help :)
Which prism is similar to a right rectangular prism with a length of 5.2 units, a width of 2 units, and a height of 3 units?
Answer:
The second rectangle on edg
Step-by-step explanation:
Answer: B.) (2nd choice)
h=1.5
w=1
l=2.6
Step-by-step explanation:
the meaning of logarithm
Answer:
the meaning of logarithm is a quantity representing the power to which a fixed number (the base) must be raised to produce a given number.
Step-by-step explanation:
: )