Is the function even or odd?

Is The Function Even Or Odd?

Answers

Answer 1

Answer:

[tex]f(\theta)=\cos(\theta)[/tex] is an even function.

Step-by-step explanation:

Recall when it means when a function is even or odd. An even function has the following property:

[tex]f(-x)=f(x)[/tex]

And an odd function has the following property:

[tex]f(-x)=-f(x)[/tex]

So, let's test some values for cos(x).

Let's use π/3:

[tex]f(\pi/3)=\cos(\pi/3)[/tex]

From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).

Now, let's find -π/3. This is the same as 5π/3. Thus:

[tex]f(-\pi/3)=\cos(-\pi/3)[/tex]

And again from the unit circle, we can see that this is 1/2.

Therefore, despite the negative, the function outputs the same value.

Cosine is an even function.

Notes:

Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!


Related Questions

How do you find the domain and range of a function and write it in set notation? What is the process of finding it? Tips and tricks are very much appreciated. I literally have no clue how to get them. Send help?

Answers

Answer:

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis

Step-by-step explanation:

plz forgive me if my answer is wrong

Domain = looking for the very far left value and the very far right value on the x-axis, and only x-axis, so the farthest left x-axis value and the farthest right x-axis value.

Range = very bottom y-value, and very top y-value

In both cases, if the arrows extend forever then that means you could have the value of infinity.

Rodney rented a machine for $70.00 to make popcorn at a school event. In addition to the machine rental cost, the popcorn supplies cost him $0.15 per bag sold. Rodney sold the popcorn for $1.00 per bag. How much profit did Rodney make if he sold 200 bags of popcorn?

Answers

Answer:

100$

Step-by-step explanation:

he profit from 1 popcorn=0.85$

from 200=170$

170$-70$=100

Answer: 100 dollars

Step-by-step explanation:

−2, −1, 0, 1 Which pair of numbers has a sum of zero? A . 1, −1 B. −2, 0 C.−2, 1 D.−1, 0

Answers

it would be A because 1 - 1 = 0

Answer:

The correct answer i would think would be A. 1 + -1= 0

Step-by-step explanation:

Sally spends 90% of her weekly income on rent. If her rent is $720 each week, find her weekly income.

Answers

Answer:

  $800

Step-by-step explanation:

We are told that ...

  0.90 × (weekly income) = $720

Dividing by 0.90 gives ...

  (weekly income) = $720/0.9 = $800

Sally's weekly income is $800.

Solve:
Please help solve the equation 1.5x-0.5=x+3.25

Answers

Answer:

x = 7.5

Step-by-step explanation:

Step 1: Subtract x from both sides.

1.5x−0.5−x=x+3.25−x

0.5x−0.5=3.25

Step 2: Add 0.5 to both sides.

0.5x−0.5+0.5=3.25+0.5

0.5x=3.75

Step 3: Divide both sides by 0.5

0.5x ÷ 0.5 = 3.75 ÷ 0.5

Hoped this helped!

☆*: .。. o(≧▽≦)o .。.:*☆

Which of the following is the set of all points in a plane that are a given distance from a point? A.Angle B.Circle C.Line D.Ray

Answers

Answer:

Circle

Step-by-step explanation:

just took test and got it correct

Circle is the set of all points in a plane is equidistant at a given distance from a point.

What is circle?

A circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called “center”.

Since, we know that

A two dimensional figure in which the set of all the points in a plane is equidistant from a given is called circle.

Therefore, option B is correct.

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A recipe needs a ratio of 2.5 of sugar to flour. If Joe uses 60g of sugar, how much flour should he use?

Answers

Answer:24



Explanation for equation:

Answer:

150 g

Step-by-step explanation:

The 2 part of the ratio represents 60 g , thus

60 g ÷ 2 = 30 g ← value of 1 part of the ratio, then

5 parts = 5 × 30 g = 150 g ← amount of flour required

you answer should be a polynomial in standard form (x- 4) ( x + 7)​

Answers

the answer is -3x-28
(x-4) (x+7)
= x•x + 7x - 4x - 4 + 7
= x*2 + 7x - 4x - 28
= x*2 + 3x - 28

Perform the indicated operation.

Answers

Answer:

-22

Step-by-step explanation:

-18 - 4 =

We are subtracting both number so add them and then give them a negative sign

-( 18+4)

-22

Answer:

-22

Step-by-step explanation:

Simplify ( 2^5/3^2)^4

Answers

Answer:

[See Below]

Step-by-step explanation:

✦ First simplify parts of the equation to make it easier:

  ✧ 2⁵ = 32

  ✧ 3² = 9

✦ Rewrite and solve parenthesis:

  ✧ (32 ÷ 9)⁴ = 3.55555556⁴

✦ Now solve the exponent:

  ✧ 3.55555556⁴ = 159.819541

✦ Simplify your answer:

  ✧ 159.82 (I rounded to the nearest hundredths)

~Hope this helps Mate. If you need anything feel free to message me.

The change in kinetic energy (in joules) as a horse accelerates from canter to gallop is found using the expression 1/2 times 350 times (12 2 Minus 6 2

Answers

Answer:

[tex]\mathtt{\Delta K.E = 10500 \ J}[/tex]

Step-by-step explanation:

Given that:

the expression for the change in kinetic energy = [tex]\dfrac{1}{2} \times 350 \times ( 122 -62)[/tex]

Recall that

Kinetic energy K.E = [tex]\dfrac{1}{2}mv^2[/tex]

where,

m = mass of the horse

v = velocity of the horse

The change in kinetic energy between  two instant times can be expressed by the relation

[tex]\Delta K.E = K.E_2 - K.E_1[/tex]

[tex]\Delta K.E =\dfrac{1}{2}mv^2_2- \dfrac{1}{2}mv^2_1[/tex]

[tex]\Delta K.E =\dfrac{1}{2}m(v^2_2-v^2_1)[/tex]

where;

m = 350

[tex]v_2[/tex] = 122

[tex]v_1[/tex]= 62

[tex]\Delta K.E =\dfrac{1}{2} \times 350 \times (122-62)[/tex]

[tex]\Delta K.E =\dfrac{1}{2} \times 350 \times (60)[/tex]

[tex]\Delta K.E = 350 \times 30[/tex]

[tex]\mathtt{\Delta K.E = 10500 \ J}[/tex]

It takes 2 gallons of milk to make a batch of ice cream. How many gallons of milk does it take to make 15.2 batches of ice cream?

Answers

Answer:

30.4

Step-by-step explanation:

2 times 15.2

Larry pours 11 gallons of water equally into 4 containers. Which equation shows how to find how many gallons of water there are in each container? A. B. C. D.

Answers

Answer:

2 3/4 gallons in each container

Step-by-step explanation:

Gallons of water = 11

Containers = 4

Larry pours 11 gallons of water equally into 4 containers

Gallons of water in each container = Total gallons of water / number of containers

= 11 / 4

= 2 3/4

There are 2 3/4 gallons of water in each containers

The equation is

Gallons of water in each container = Total gallons of water / number of containers

w-5<17 solve the inequality for w

Answers

Answer:

w < 22

Step-by-step explanation:

w - 5 < 17

Add 5 to both sides:

w - 5 + 5 < 17 + 5

w < 22

Mia is taking a multiple choice test with a total of 50 points available. Each question is worth exactly 2 points. What would be Mia's test score (out of 50) if she got 3 questions wrong? What would be her score if she got x questions wrong?

Answers

Answer:

Mia's test score is 44 if she got 3 questions wrong.

Mia's test score is (50-2x) if she got x questions wrong.

Step-by-step explanation:

It is given that, Mia is taking a multiple choice test with a total of 50 points available. Each question is worth exactly 2 points.

If she got 3 questions wrong, then

Deducted marks [tex]=2\times 3=6[/tex]

Marks obtained by Mia = Total marks - Deducted marks

                                      [tex]=50-6[/tex]

                                     [tex]=44[/tex]

So, Mia's test score is 44 if she got 3 questions wrong.

If she got x questions wrong, then

Deducted marks [tex]=2\times x=2x[/tex]

Marks obtained by Mia = Total marks - Deducted marks

                                      [tex]=50-2x[/tex]

So, Mia's test score is (50-2x) if she got x questions wrong.

This is true of false??​

Answers

Answer:

It's TRUE!

CLOSURE PROPERTY IS USED !

Please help me out please!!!!!!

Answers

Answer:

  you're nearly there

x/4, x/44x, 4x

Step-by-step explanation:

You have obviously determined the correct entry in the top box of each pair. What you seem to have failed to observe is that the bottom box in each pair needs exactly the same entry as the top box.

_____

You figure this out by looking at the stuff that is outside the box. The numbers and symbols for the second box show how the function indicated outside the first box is evaluated. That is f(x) at the top becomes 4x at the bottom, where x (in this case) is x/4 for both.

helpppp

Which of the following statements is the most precise and correct to define perpendicular lines?
A. Two lines are perpendicular if they intersect.
o
B. Two lines are perpendicular if they meet at a single point such that the two lines make a "T".
o
C. Two lines are perpendicular if they meet at one point and one of the angles at their point of
intersection is a right angle.

Answers

Answer:

C

Step-by-step explanation:

you can add that they meet at a 90° angle

Here is a list of numbers:
9, 3, 15, 19, 4, 2, 18,8,13
State the median.

Answers

Median is the middle number in a sorted list of numbers so in your question the number in the middle is 4 so the median is 4.

Please help and show your work TwT

Answers

Answer:

Step-by-step explanation:

First we solve 5(x + 2) ≥ 2(x + 8).

5x + 10 ≥ 2x + 16

3x ≥ 6

x ≥ 2.

Now we place an equal sign into the box:

4(x - 6) = 2(x - 10)

4x - 24 = 2x - 20

2x = 4

x = 2.

For the solution to only have 1 value, the solution must be x = 2.

Therefore we must have x ≥ 2 and x ≤ 2.

Nick and Pam are paid $38.25 for their work network one hour and five minutes and Pam work three hours they split the money according to the amount of time each of them worth how much is make sure of the money explain

Answers

Answer:

Nick get = $10

Pam get = $28.25

Step-by-step explanation:

Given:

Total amount paid = $38.25

Nick work = 1 hour 5 minutes = 1.0833 hr

Pam work = 3 hour

Find:

Amount they get

Computation:

Assume each get x in 1 hour

So,

3x + 1.0833x = 38.25

4.0833x = 38.25

x = 9.3674

Nick get = 1.0833(9.3674) = 10.14 = $10

Pam get = $38.25 - $10 = $28.25

I dont understand this can you help​

Answers

Answer:

C

Step-by-step explanation:

To answer a multiple choice question process of elimination can be very helpful

A isnt correct because CED is 90 degrees

B isnt correct since the line equals 180 degrees

C is correct because CED and AEC are a linear pair that add up to 180 degrees so if CED is 90 then so is AEC

Answer:

i did not understand it either

Step-by-step explanation:

but it means so like you would see what statement is ture so like say ced measured right then you would say it is right, you want to see what angel is right with this question your answer is the third answer

hope this help

5.3x10 4 in standard form.

Answers

Answer:

5.3× 10⁴= ?

Step-by-step explanation:

10⁴ can also be written as 10×10×10×10= 10000

so, 5.3 × 10000= 53000

Scientific notations are the way through which a very small or a very large number can be written in shorthand. The value of 5.3×10⁴ in standard form is equal to 53,000.

What are Scientific notations?

Scientific notations is the way through which a very small or a very large number can be written in shorthand.  In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

Given the numerical value 5.3×10⁴ which is needed to be written in the standard form, therefore, we can write,

5.3 × 10⁴

= 5.3 × 10,000

= 53,000

Hence, the value of 5.3×10⁴ in standard form is equal to 53,000.

Learn more about Scientific notation here:

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??? help plssss ???? ​

Answers

Answer:

18

Step-by-step explanation:

12(3/2)=36/2=18

Answer:

18

Step-by-step explanation:

[tex]12\left(\frac{3}{2}\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=12\times \frac{3}{2}\\\\\mathrm{Multiply\:fractions}:\quad \:a\times\frac{b}{c}=\frac{a\:\times\:b}{c}\\=\frac{3\times\:12}{2}\\\\\mathrm{Multiply\:the\:numbers:}\:3\times\:12=36\\=\frac{36}{2}\\\\\mathrm{Divide\:the\:numbers:}\:\frac{36}{2}=18[/tex]

In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now? In 3 years, Dianna will be 4 times as old as she was 33 years ago. How old is Dianna now?

Answers

Answer:

x = 45

45 years old

Step-by-step explanation:

x + 3 = 4(x - 33)

x + 3 = 4x - 132

x - 4x = - 132 - 3

-3x = -135

x = -135/-3

x = 45

Combine the like terms to create an equivalent expression:
8t+1+(−4t)+(−6)

Answers

Answer:

4t-5

Step-by-step explanation:

Answer:

4t-5

Step-by-step explanation:

8t+1+(-4t)+(-6)

= 8t+(-4t)+1+(-6)

=(8t-4t)+(1-6)

=(8-4)t+(-5)

=(4)t+(-5)

=4t-5

what is the solution to the equation 1/x=x+3/2x^2

Answers

Answer:

3.

Step-by-step explanation:

1/x = (x+3)/(2x^2), where x ≠ 0.

Cross-multiply to give 2x^2 = x(x+3).

2x^2 - x^2 - 3x = 0

x^2 - 3x = 0

x(x - 3) = 0

x = 3 or x = 0 (rejected because equation will be undefined)

Answer:

d

Step-by-step explanation:

The population of Austin, Texas, was about 494,000 at the beginning of a decade. The population increased by 3% each year. Write an exponential growth model that represents the population y (in thousands) t years after the beginning of the decade. Find and interpret the y-value when t = 10.

Answers

Answer:

y(t) = 494 (1.03)^t

y(10) = 663,89

Step-by-step explanation:

An increase in population by 3% each year means that at the end of each year, the population is 1.03 times what it was at the start of the year

This increase in population continues for t years

Exponential growth model that represents the population y (in thousands) t years after the beginning of the decade is

y(t) = 494 (1.03)^t

Where,

y = population

t = number of years

Find y when t = 10

y(t) = 494 (1.03)^t

y(10) = 494 (1.03)^10

= 494 ( 1.3439)

= 663.8866

Approximately y(10) = 663.89

This means that after 10 years from when the population was 494,000, it increased to 663,89.

What is the answer for 2/3 x -4 = -2

Answers

Answer:

x=3

Step-by-step explanation:

2/3x -4 = -2

2/3x = 2

(3/2)*(2/3x) = (2*3/2)

x=3

Answer:

x=3 I hate asking for things but may  i have brainliest I need to rank up

Step-by-step explanation:

Step 1: Add 4 to both sides.

2/3x−4+4=−2+4

2/3x=2

Step 2: Multiply both sides by 3/2.

(3/2)*(2/3x)=(3/2)*(2)

then you get x=3

Find the distance between the points (-16,10) and (2,-14)

Answers

Answer:  The distance is 30

Step-by-step explanation:

To find the distance between the two points,find the difference between the x and y values, square them and add them to find their square root.

10 - (-14) = 24

-16 - 2=   -18

24^2 + 18^2 = d^2  where d is the distance

576 + 324 = d^2  

900 =d^2

d = [tex]\sqrt{900}[/tex]

d= 30

Answer:

d=30

Step-by-step explanation:

distance between 2 points: d

d=√(x2-x1)²+(y2-y1)²     (-16,10) and (2,-14)

d=√(2-(-16)²+(-14-10)²

d=√18²+(-24)²

d=√324+576

d=√900

d=30

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