Explain why arctan(1) = 45° or π/4.

Answers

Answer 1

Answer:

Explanation below

Step-by-step explanation:

Inverse Trigonometric Functions

They are defined as the inverse of the basic trigonometric functions which are sine, cosine, tangent, cotangent, secant, and cosecant.

The corresponding inverse functions are called arcsin, arccos, arctan, arccot, arcsec, arccsc.

These inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios.

For example,

[tex]\displayystyle \sin 30^\circ=\frac{1}{2}[/tex]

Then:

[tex]\displaystyle arcsin \frac{1}{2}=30^\circ[/tex]

Since:

[tex]\tan 45^\circ=1[/tex]

Or, equivalently:

[tex]\displaystyle \tan \frac{\pi}{4}=1[/tex]

Then:

[tex]\displaystyle arctan(1)=45^\circ[/tex]

Or:

[tex]\displaystyle arctan(1)=\frac{\pi}{4}[/tex]


Related Questions

What is the slope of the line shown below?

Answers

Answer:

y=-1/5x+3 or slope = -1/5

Step-by-step explanation:

A toy company uses a random sample to simulate 10 toys to inspect out of 1,000. The integers 1 to 5 represent toys that are below standard. 76 68 32 2 4 35 93 61 21 51 Based on this sample, how many toys will be below standard in the whole group?
A.200

B.2

C.5

D.20

Answers

Answer:

I believe it is B. 2

Step-by-step explanation:

Gabrielle is 7 years younger than Mikhail. The sum of their ages is 41. What is Mikhail's age?

Answers

34, im not sure if its right though

Identify an equation in slope intercept form for the LINE parrelel to y=5x+2 that passes through - 6,-1

Answers

Answer:

y = 5x-1

Step-by-step explanation:

parallel lines have the same slope.

y intercept: -1

slope: 5

- 1 is the same as +-1

so, y = 5x-1

5[tex]multiply\\[/tex]

Answers

Answer:

5 multiply by wat???

Step-by-step explanation:

??? Don’t understand

I really need help so please help me out

Answers

Answer:

The answer is option 2.

Step-by-step explanation:

Given that the TU and UF added up together to form a length of 32. In order to find TU, you have to subtract length of UF from 32 :

TU + UF = 32

TU + 20 = 32

TU = 32 - 20

TU = 12

please hellppp i will mark brainliest ​

Answers

30 degrees it's right

Write 6-12 as an addition expression.

Answers

Answer:

-12 + 6

Step-by-step explanation:

Answer:

-12+6

Step-by-step explanation:

The two terms are

-12

and

+6

Put them together in the reverse order and you have -12+6

What is the distance between the points (-4, -8) and (10, -8)?

Answers

Where The Picture. ? So We Can Solve It

Answer:

14

Step-by-step explanation:

the difference between -4 and 10 is 14, (4 to get to 0, and 10 more to get to 10.) and the difference between -8 and -8 is 0 so we don’t have to count it.

PLEASE HELP!!!!!!! 17 POINTS AND BRAINLIEST

Answers

Answer:

I got c

Step-by-step explanation:

it came out to be a fraction of y=3/2x - 2

I think the answer is c

the shop keeper at an inn receives 175 letters a week (7 days). How many letters does he receive in a day

Answers

Answer:

25

Step-by-step explanation:

175 divided by 7 =25

Answer:

25 letters

Step-by-step explanation:

the word problem can be expressed as 175=7x

there are 7 days in a week and you want to find home many there are in one of those days

divide 175 by 7, your answer is 25.

Describe the nature of the roots for the equation
49x2– 28x +4 = 0

Answers

Answer:

The roots of the equation is real and repeated

Step-by-step explanation:

Here, we want to describe the nature of the roots of the given quadratic equation

To get the nature of the roots, we find the discriminant of the equation

The discriminant is;

b^2 - 4ac

In this case, b = -28 , a = 49 and c = 4

The discriminant is thus;

-28^2 - 4(49)(4)

= 784 - 784 = 0

Since the discriminant is zero, this means that the quadratic equation has real roots which are the same

what is 8+8? IM CRYING PLS. WILL GIVE BRAINLIEST. I DONT KNOW IVE BEEN UP ALL NIGHT STRESSING PLEASE.

Answers

Answer:

Hey buddy, here is your answer. Hope it helps you.

Step-by-step explanation:

8+8=16.

16 lol step by step : 8+8:16

can someone just please answer my question I rlly need it​

Answers

Answer:what is the question?

Step-by-step explanation:what is it?

What is the answer 5x² – 33x - 14 = 0​

Answers

Answer:

X=-2/5,7

Step-by-step explanation:

5x² – 33x - 14 = 0​

5x^2-(35-2)x-14=0

5x^2-35x+2x-14=0

5x(x-7)+2(x-7)=0

(5x+2)(x-7)=0

X=-2/5,7

so the value of X is -2/5,7

Juan's cell phone company charges $35 a month for phone service plus
$0.50 for each text message. How many text messages does Juan send in a
month if his bill was $52?

Answers

The Answer is x=34.cvoddievx

Answer:

Juan sends 34 text messages.

Step-by-step explanation:

$52-$35= $17

17 dollars / .50 = 34 messages

Solve this system of equations by graphing. First graph the equations, and then type the solution. y=2x+2 y=x–2

Answers

Answer:

(-4,-6)

Step-by-step explanation:

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

The point of intersection between the two equations is (-4, -6).

The graph is given below.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 6 is an equation.

We have,

y = 2x + 2

y = x - 2

Now,

The point of intersection.

2x + 2 = x - 2

2x - x = -2 - 2

x = -4

Putting in y = 2x + 2

y = 2 x -4 + 2

y = -8 + 2

y = -6

(-4, -6) is the point of intersection.

Now,

The graph of the equation is given below.

Thus,

The point of intersection between the two equations is (-4, -6).

The graph is given below.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

In the first quarter of a football game, the Tech Tigers gained 7 yards on every play, moving closer to the Knights' goal line. They are now on their own 25-yard line. On what yard line were the Tigers 3 plays ago?

Answers

Answer:

they were on the 21-yard line

Step-by-step explanation:

Answer:

4-yard line

Step-by-step explanation:

i got this answer correct on my quiz so the other answer is wrong

solve for n
-112 = 7n

Answers

Answer:

n= -56/3

Step-by-step explanation:

Answer:

n -112 = 7n

Step-by-step explanation:

-6n=  112

-3n=  56

n=  56/ -3

n= -56/3

Helena ate at his fraviote restaurant he received excellent service from his waitstaff and decided to leave a 22 percent tip before tip his bill came to 60 how much would the meal have cost in total including tip

Answers

Answer:

$73.20

Step-by-step explanation:

original bill: $60

Tip: 22%  $13.20

Total: $73.20

Hope this was helpful! Have a great day!

Which choices are equivalent to the fraction below? Check all that apply.
18/36

1.6/18
2.8/18
3.1/3
4.1/2
5.3/4
6.6/12

Answers

None of the following are equivalent

How many solutions does the equation below have? 2(4x + 10) = 8x+20

Answers

Answer:

There are infinite solutions

Step-by-step explanation:

2 (4x + 10) = 8x + 20

Distribute 2(4x + 10)

8x + 20 = 8x + 20

They equal each other meaning they are infinite solution

can y’all help please :)

Answers

number three ? I’m not sure

if there are 21 ladybugs how many bumblebees?​

Answers

Answer:

I need the rest of the question to answer

help me plz :) i would rly appreciate it.

Answers

Answer:

Ok i understand what this is.

Step-by-step explanation:

I will show u i just have to figure it out first.Im sorry if I cant figure it out but i will try my best to help:D

help me please . quick :)

Answers

Answer:

x= 1

QS = 10 cm

QRS = 40cm

Step-by-step explanation:

4x + 1 = 5x

x= 1 cm

QS = 4x + 1 + 5x

= 9x + 1

= 9 + 1

= 10cm

QRS perimeter

QS + RQ + RS but ( RQ = RS)

= 10 + 15 + 15

= 40cm

3(5 +6) =
can someone please help?

Answers

Answer:

33

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

3(11)=33

hope this help

6*4÷12+72÷8-9 ??

pls help ty

Answers

Answer:

2

Step-by-step explanation:

Use BODMAS(bracket, of, division, multiplication, addition and subtraction)

72/8=9

(6*4)=24

24/12+9-9

2+0

=2

The solution for the given operations of numbers is 2.

What is PEMDAS Rule?

PEMDAS rule is the same as BODMAS rule.

PEMDAS is the abbreviation for Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction.

We are using BODMAS rule here to solve the given operations.

6 * 4 ÷ 12 + 72 ÷8 - 9

According to the rule, first we should do multiplication.

6 × 4 = 24

6 * 4 ÷ 12 + 72 ÷8 - 9 = 24 ÷ 12 + 72 ÷8 - 9

Next do the division.

24 ÷ 12 = 2 and 72 ÷8 = 9

24 ÷ 12 + 72 ÷8 - 9 = 2 + 9 - 9

Now do the addition and subtraction.

2 + 9 - 9 = 2

Hence the final answer for the given operation is 2.

Learn more about PEMDAS rule here :

https://brainly.com/question/29172059

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(WILL GIVE BRAINLIEST) Solve for x.
-2(-9x+5)-4x=2(x-5)-4

Simplify your answer as much as possible

Answers

Answer:

−2(−9x+5)−4x=2(x−5)−4

Step 1: Simplify both sides of the equation.

−2(−9x+5)−4x=2(x−5)−4

(−2)(−9x)+(−2)(5)+−4x=(2)(x)+(2)(−5)+−4(Distribute)

18x+−10+−4x=2x+−10+−4

(18x+−4x)+(−10)=(2x)+(−10+−4)(Combine Like Terms)

14x+−10=2x+−14

14x−10=2x−14

Step 2: Subtract 2x from both sides.

14x−10−2x=2x−14−2x

12x−10=−14

Step 3: Add 10 to both sides.

12x−10+10=−14+10

12x=−4

Step 4: Divide both sides by 12.

12x

12

=

−4

12

x= -1/3

Step-by-step explanation:

Good luck! Hope this helps! <3

Answer :

[tex]x = - \frac{1}{3} [/tex]

or you can just write x = -0.3

hope this helps!

what are the best "never have i ever" questions? please give some good ones! (and don't report!!! i'm giving y'all 50 points ❤️) tysm

Answers

Never have I ever said ‘I love you’ just to get laid.

Answer:

never have i ever told my best friends boyfriend that she is cheating on him so i could get with him.../

(she was tho)

Step-by-step explanation:

puts finger down

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