The domain and range of trigonometric functions are as follows;
Function Domain Range
sin(x). All real numbers [-1, 1]
cos(x). All real numbers [-1, 1]
tan(x). {x| x ≠ -3•π/2, -π/2, π/2, } R
The domain and range of the inverse sine, cosine, and tangent are;
Function Domain Range
arcsin(x). (-1, 1) [-π/2, π/2]
arccos(x). (-1, 1) [0, π]
arctan(x) (-∞, ∞). [-π/2, π/2]
What are the domains and ranges of the trigonometric functions?sin(x)
The domain of sin(x) is the set of possible values for x, for which sin(x) is defined, which is;
All real numbers.The range of sin(x) is the set of possible values output values of sin(x) is, which is; -1 ≤ sin(x) ≤ 1
The range is therefore; [-1, 1]cos(x)
Similarly;
The domain of cos(x) is the set of all real numbersThe range of cos(x) is; -1 ≤ cos(x) ≤ 1tan(x)
tan(x) = sin(x)/cos(x), however, cos(x) = 0, when x = -3•π/2, -π/2, π/2, 3•π/2...
The domain of tan(x) is therefore;
{x| x ≠ -3•π/2, -π/2, π/2, 3•π/2...}sin(x) increases as cos(x) decreases, therefore;
The range of tan(x) = sin(x)/cos(x) is therefore;
-∞ < tan(x) < ∞ which is {-∞, ∞}arcsin(x)
The input of arcsin(x) is sin(x)
sin(x) = opposite/hypotenuse
Given that the magnitude of hypotenuse > opposite, the ratio, opposite/hypotenuse is < 1 in magnitude
The domain of arcsin(x) is therefore;
-1 < sin(x) < 1, which is (-1, 1)The range is the set of possible outputs, which is [-π/2, π/2], given that sin(x) is positive and negative from -π/2, π/2
The range is [-π/2, π/2]arccos(x)
Similarly;
The domain of arccos (x) is (-1, 1) The range is [0, π]arctan(x)
The input of arctan(x) is tan(x)
tan(x) = sin(x)/cos(x)
The domain of arctan(x) is therefore;
{-∞, ∞}The range is [-π/2, π/2]Learn more about the domain and range of functions here:
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Find the perimeter of triangle ABC rounded to the nearest whole number. A (-1,4) B (2,2) and C (-2,-1)
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-1}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{2}) ~\hfill AB=\sqrt{(~~ 2- (-1)~~)^2 + (~~ 2- 4~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 3)^2 + ( -2)^2}\implies \boxed{AB=\sqrt{13}} \\\\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{2})\qquad C(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1}) ~\hfill BC=\sqrt{(~~ -2- 2~~)^2 + (~~ -1- 2~~)^2}[/tex]
[tex]~\hfill BC=\sqrt{( -4)^2 + ( -3)^2}\implies \boxed{BC=5} \\\\\\ C(\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad A(\stackrel{x_2}{-1}~,~\stackrel{y_2}{4}) ~\hfill CA=\sqrt{(~~ -1- (-2)~~)^2 + (~~ 4- (-1)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( 1)^2 + (5)^2}\implies \boxed{CA=\sqrt{26}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{\sqrt{13}~~ + ~~5~~ + ~~\sqrt{26} ~~ \approx ~~ \text{\LARGE 14}}[/tex]
Use the figure to the right to find the value of PT.
PT= 4x+4 and TQ 6x-6
HELP !!
Elena and Diego each wrote equations to represent these diagrams. For each diagram decide which equation you agree with, and solve it. You can assume that angles that look like right angles are indeed right angles.
Elena: X=35
Diego: X+35=180
Answer: Diego is correct, and X = 145
Step-by-step explanation:
The line that 35* and x* rest on must equal 180*. Elena cannot be right if we assume this, as 35 + 35 = 70. We must then move onto Diego's formula.
[tex]X + 35 = 180[/tex]
[tex]180 - 35 = X[/tex]
[tex]X = 145[/tex]
Solving this, we would subtract 35 from 180, leaving us with 145*. This must be correct as the solution would give us the total we need.
The ratio of red marbles to blue marbles in a jar is 5:2. The total number of marbles is 21. What is the
smaller amount of marbles in the jar?
Answer:
6
Step-by-step explanation:
Solve y- 15 =-3.
A-12
B 12
C-18
D-18
Answer:
B
Step-by-step explanation:
y - 15 = -3
add 15 to both sides to get:
y=12
Pls pls help whoever gets it right gets a crown
Answer: 12.8x^2
Step-by-step explanation:
3.2x * 4x=
3.2 * x * 4 * x=
3.2 * 4 * x * x=
12.8 * x^2=12.8x^2
What is this supposed to mean!?!?!?!?
Answer:
h = V/B
Step-by-step explanation:
[tex]\sf V \div B = h\\Reverse\\h = V \div B[/tex]
Answer:
D. h = V/B
Step-by-step explanation:
"Solve...for h" means get h all by itself on one side of the equation.
V = Bh
Divide both sides by B.
V/B = h
Turn it around and you can see the answer in the choices. D. h = V/B is the correct answer.
QUESTION 1 1. The Geography club at a school collected empty cans of soft drinks for recycling for a period 20 school days. The number of cans collected was recorded and the data is given below: 48 50 52 59 60 68 73 76 76 76 78 79 80 81 82 82 84 91 92 98 1.1.calculate the average nunmber of the cans collected
1.2. Calculate the average number of the cans collected. Determine the median number of cans collected. Determine the lower and the upper quartiles. 1.3. 1.4. Represent the data in a box and whisker diagram. 1.5. Determine the range of the data. C ( au table underne
Answer:
Step-by-step explanation:
a marketing firm does a survey to find out how many people use a product. to accomplish this, they select a random sample of one hundred people consumers and record how many use the product.
The given situation is an example of an Observational Study.
What is an Observational Study?In observational studies, the impact of a risk factor, diagnostic test, treatment, or other intervention is observed without an attempt to alter who is or is not exposed to it. There are two categories of observational studies: cohort studies and case control studies.
Cohort study: Any group of people who are connected in some way constitutes a cohort for research purposes. For instance, a birth cohort is made up of all individuals born within a specific period of time. Researchers contrast the outcomes for cohort members who have been exposed to a specific variable with those for cohort members who have not.
Case control study: In this method, researchers choose individuals who already have a health issue (referred to as "cases") and a control group that is similar but free of the issue.
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Find the area of the composite figure.
8 cm
10 cm
14 cm
Answer:
96 cm
Step-by-step explanation:
14-10= 4.
So the base of the triangle is 4.
10*8=80
4*8*1/2=16
80+16 = 96
Answer:
32
Step-by-step explanation:
solve the equation 4x -6 = 22
Answer: x=7
Step-by-step explanation: hope this helps!!!
Answer:
x=7
Step-by-step explanation:
point k is on a line segment JL. given JK =2x-2, KL =x-9, and JL = 2x+8, determine the numerical length of KL
The numerical length of KL = 10.
What exactly is an equation?An equation, in its most basic form, is a mathematical statement demonstrating that two mathematical expressions are equal.3x + 5 = 14, for example, is an equation in which the expressions 3x + 5 and 14 are separated by a 'equal' sign.So,
JK + KL = JL2x – 2 + x – 9 = 2x + 8Combine similar terms:
3x -11 = 2x+8Take 2x off each side:
3x-2x -11 = 2x+8-2xx-11 = 8Add 11 for each side:
x-11+11 = 8+11x = 19KL = x – 9KL = 19-9KL = 10Therefore, the numerical length of KL = 10.
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If 3x=12, then x=4 What property is it
Answer:
correct
3x4=12
Step-by-step explanation:
A truck can be rented from company a for $110 a day plus $0.70 per mile, company b charges $80 a day plus $0.80 per mile to rent the same truck. find the number of miles in a day at which the rental costs for company a and company b are the same.
The number of miles for same rental costs are 300 miles.
Let the number of miles be x.
Firstly calculating the cost of Company a -
Total cost = One day cost + Number of miles × Cost per mile
Total cost = 110 + 0.70x
Calculating the cost of Company b -
Total cost = One day cost + Number of miles × Cost per mile
Total cost = 80 + 0.80x
Now, for the same rental cost, we will equate the two expressions. This will calculate the value of x.
110 + 0.70x = 80 + 0.80x
Rearranging the expression -
110 - 80 = 0.80x - 0.70x
Performing subtraction
30 = 0.10x
Shifting the values on other side of equation
x = 30/0.10
Performing division
x = 300
Hence, the rental cost for both companies will be same for 300 miles.
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Which figure is missing in the pattern?
?
Answer:
B
Step-by-step explanation:
it grows b
Which expression demonstrates how the Distributive Property could be used to find the product of 5 and 48?
A. 5 (50) − 2
B. None of these
C. 50 − 5 (2)
D. 5 (50) + 5 (2)
E. 5 (50 − 2) + 5 (2)
HELP ME PLEASEEEE!!!!!
Which square root could be the number shown on the number line?
O A. √15
O B. √17
O C. √26
O D. √24
The number shown on the number line could be related to the inexact irrational number √17.
What irrational number is associated with a point on a number line?
In this problem we find the location of a point on a number line, which is related to an inexact irrational number, that is, an irrational number that is not equivalent to any rational number. The point is between two exact irrational numbers, that is, √16 = 4 and √25 = 5.
There are two options: (i) √17, (ii) √24. √24 is close to 5, but √17 is close to 4. Thus, the number shown on the number line could be related to the inexact irrational number √17.
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Triangle ABC is transformed to triangle A′B′C′, as shown below: A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 3, 4, B at ordered pair negative 4, 2, C at ordered pair negative 1, 1. A triangle A prime B prime C prime has A prime at ordered pair 3, 4, B prime at ordered pair 4, 2, C prime at ordered pair 1, 1. Which equation shows the correct relationship between the measures of the angles of the two triangles? (1 point) a The measure of angle ABC = The measure of angle A prime B prime C prime b The measure of angle ABC = The measure of angle B prime C prime A c The measure of angle BCA = The measure of angle A prime B prime C prime d The measure of angle BCA = The measure of angle C prime A prime B prime
The correct relationship between the angles of the two triangles is as follows:
Angle measurement BCA = Angle C prime A prime B measurement.What is a triangle?A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same.So, in an ABC triangle, A is at ordered pair negative 1, 3, B is at ordered pair 0, 1, and C is at ordered pair negative 3, 0.
A triangular shape A prime, B prime, and C prime all have A prime at ordered pair minus 1, minus 3, B prime at ordered pair minus 1, and C prime at ordered pair minus 3, 0.Then,
<BAC = <B'A'C'<ABC = <A'B'C'<ACB = <A'C'B'Angle measurement BCA = Angle C prime A prime B measurement.
Therefore, the correct relationship between the angles of the two triangles is as follows:
Angle measurement BCA = Angle C prime A prime B measurement.Know more about triangles here:
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Tyrell has a box of colored pencils. He uses 65 pencils and has 114 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
p − 65 = 114
p = 114 − 65
65 + p = 114
114 + p = 65
Answer:
p-65=114
Step-by-step explanation:
In this equation, "p" is the amount of pencils in the box before he starts drawing. he removes 65 pencils from the box, leaving 114 in the box. What he needs with 65 pencils at once, I can't fathom.
The Rock Club members have collected 182 gems. How many did each
member collect if
a) Alice collected 1 more than 3 times what Cecil did.
b) Jaime collected 12 less than 3 times what Alice did.
c) Amir collected 10 less than Cecil.
d) Monte collected 5 more than Cecil.
How many gems didCecil collect?
How many gems did Alice collect?
How many gems did Jaime collect?
How many gems did amir collect
How many gems did Monte collect
Using a system of equations, the amounts of gems collected by each member is are given as follows:
Cecil: 13Alice: 40Jaime: 108Amir: 3Monte: 18.What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Number of gems collected by Cecil.Variable y: Number of gems collected by Alice.Variable z: Number of gems collected by Jaime.Variable t: Number of gems collected by Amir.Variable w: Number of gems collected by Monte.They collected a total of 182 gems, hence:
x + y + z + t + w = 182.
Alice collected 1 more than 3 times what Cecil did, hence:
y = 3x + 1.
Jaime collected 12 less than 3 times what Alice did, hence:
z = 3y - 12 = 3(3x + 1) - 12 = 9x - 9.
Amir collected 10 less than Cecil, hence:
t = x - 10.
Monte collected 5 more than Cecil, hence:
w = x + 5.
Replacing everything in the first equation, we can solve for x as follows:
x + y + z + t + w = 182.
x + 3x + 1 + 9x - 9 + x - 10 + x + 5 = 182.
15x = 195
x = 195/15
x = 13.
Hence the other variables are:
y = 3(13) + 1 = 40.z = 9x - 9 = 9(13) - 9 = 108.t = x - 10 = 13 - 10 = 3.w = x + 5 = 13 + 5 = 18.Thus the amounts of gems collected by each member is are given as follows:
Cecil: 13Alice: 40Jaime: 108Amir: 3Monte: 18.More can be learned about a system of equations at https://brainly.com/question/24342899
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If f (x) = 2 x + 5 and three-halves are inverse functions of each other and StartFraction 41 Over 8 EndFraction,
The value of the inverse function f⁻¹(8) is [tex]\frac{3}{2}[/tex] .
An inverse function in mathematics is a function that "undoes" another function.
In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f⁻¹ .To calculate the inverse of the function f (x) = 2 x + 5 we simply write the function in the form y = 2x + 5 .
Now we solve the equation for x.
∴ y = 2x + 5
or, 2x = y-5
or, x = (y-5)/2
Hence the inverse of the function is given as:
f⁻¹ (x) = (x - 5 ) / 2
Now we have to find the value of f⁻¹ (8).
f⁻¹ (8) = (8-5) / 2
or, f⁻¹ (8) = 3 / 2
Hence the value of f⁻¹ (8) is 3 / 2 .
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Disclaimer: the complete question is:
If f (x) = 2 x + 5 and three-halves are inverse functions of each other and f(x)=2x+5, what is f-1(8)?
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Answer: B
Step-by-step explanation: On Edge 2022
If point A (-5, 9) is reflected across the x-axis, what will be the new coordinates of the image, A'?
please help! I am in the middle of a test! I am offering 30 points.
The new coordinates of the image A' will be (-5, -9).
Here, we are given a point on the cartesian plane- A (-5, 9)
It is reflected along the x axis to form a new point A'
Originally, we can see that the point A will be in the 2nd quadrant as x is negative and y is positive.
Now, when it is reflected across the x axis, the point will shift from the 2nd quadrant to the 3rd quadrant.
In the third quadrant, both x and y values are negative. Thus the coordinates of the reflected point A' will become (-5, -9).
Note that the absolute values of the point will not change when it is reflected. It is only the signs that change.
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- 3x + 6y =- 18 solve for y
Answer:
y = [tex]\frac{1}{2}[/tex] x - 3
Step-by-step explanation:
- 3x + 6y = - 18 ( isolate the term in y by adding 3x to both sides )
6y = 3x - 18 ( divide through by 6 )
y = [tex]\frac{1}{2}[/tex] x - 3
WILL GIVE 14 POINTS AND BRAINLIEST IF ANSWERED PROPERLY WITH NO SPAM
Answer:
B, C, A
Step-by-step explanation:
B, C, A
The pair of triangles that are congruent by the ASA criterion is . The pair of triangles that are congruent by the SAS criterion is .
The relationship between the triangles are;
Δ ABC and Δ XYZ is related by ASA
Δ BAC and ΔRQP are related by SAS
What is congruency of triangles?The term congruency has to do with the fact that the triangles are similar. That is why another way that we could express congruent triangles is to call them similar triangles. These are the triangles that look alike in some ways. The triangles may be similar in the following ways;
1) Angle Angle Side
2) Side Side Side
3) Side Angle Side
4) Angle Side Angle
5) Angle Side Side
Having seen the various ways in which triangle could be similar we are asked to obtain the triangles that are similar by Angle Side Angle and Side Angle Side.
A good look at the triangles as shown in the image attached to this answer would show us which of the triangles are similar on the basis of Angle Side Angle and Side Angle Side.
We can see that;
Δ ABC and Δ XYZ is related by ASA
Δ BAC and ΔRQP are related by SAS
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5 Bruno buys 9.625 gallons of gasoline at a gas station.
Each gallon costs $3.40. Bruno also buys a bag of ice
for $3.99. How much in total does Bruno spend at the
gas station to the nearest cent?
Answer:
Step-by-step explanation:
9.625 rounded is 10.
10 x $3.40 = $34
$3.99 rounded to the nearest cent is $4.
$34 + 4 = $38, so Bruno spends about $38 total.
Complete the sentence.
32 g≈ ___ oz
32g = 1.12877oz or 32 grams is equivalent to 1.12877 ounces.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
A conversion factor is a number used to change one set of units to another, either by multiplying or dividing.
The sentence states an equality between units of weight: grams and ounces.
From there, we can say that we are asked how many ounces are there in 32 grams.
Converting grams to ounces, we must use the conversion
1 gram = 0.035274 ounces
32 grams = 32 (0.035274 ounces)
32 grams = 1.12877 ounces
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Which line is perpendicular to y=−3x+2?
A. y = −3x+1/2
B. y =−1/3x+1
C. y = 3x−1/2
D. y =1 /3x−1
(Note: the selected answer is not guaranteed to be correct in the image)
Answer:
I kinda want to say it's C
Which length in cm should be recorded for the red line in the figure above
Answer:
3 ins 2 cm
Step-by-step explanation:
What is the least common denominator of 5/8 and 1/6
Answer:
24
Step-by-step explanation:
Equivalent fractions with the LCD
5/8 = 15/24
1/6 = 4/24