Explain why arctan(1) = 45 or /4.

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

determine the equation of the line given by the graph.

a) y=2/3x -1
b) y=3/2x -1
c) y= -2/3x -1
d) y= -3/2x -1

Answers

Answer:

Step-by-step explanation:

a) Y= 2/3X-1

Find the measure of each numbered angle

Answers

measure of angle 1 is 56
measure of angle 2 is 56
measure of angle 3 is 74

All triangle’s angles add up to 180

The measure of each numbered angles are ∠1 = 56°, ∠2 = 56° and ∠3 = 74°.

What is Angle?

An angle for any figure is formed by two rays which joins at a common point called vertex or node.

Usually angles are measured in degrees or radians.

Consider triangle PMQ

The sum of the interior angles of a triangle is 180°.

∠MPQ + ∠QMP + ∠PQM = 180°

58° + 66° + ∠1 = 180°

∠1 = 180° - (58° + 66°)

∠1 = 180° - 124°

∠1 = 56°

Now, ∠1 and ∠2 are vertically opposite angles. Hence they are equal.

∠2 = 56°.

Again, for triangle NQO

∠2 + ∠3 + 50° = 180°

56° + ∠3 + 50° = 180°

∠3 = 180° - (50° + 56°)

∠3 = 180° - 106°

∠3 = 74°

Hence ∠1, ∠2 and ∠3 are 56°, 56° and 74° respectively.

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The ratio table below shows the conversion between centigrams and milligrams. How many centigrams would be equal to 0.3 milligram?

Answers

Answer:

.03

Step-by-step explanation: because milligrams is 10 times as much as centimeters so if thereś .3 milligrams then you divide .3 by 10 and youĺl get .03

Which translation takes y = | x + 2 | - 1 to y = | x | + 2 ?

Select one:
a. 2 units left, 3 units down
b. 2 units left, 3 units up
c. 2 units right, 3 units up
d. 2 units right, 3 units down

(Solve by graphing and determining the translation. Thanks in advance!)

Answers

Answer:

Step-by-step explanation:

y = | x + 2 | − 1 has a vertex at (-2, -1).

y = | x | + 2 has a vertex at (0, 2).

So the graph is translated 2 units right and 3 units up.

How much money must be deposited to earn $219 in simple interest in 8 years at an annual rate of 6.2%?

Answers

Answer: $1,147.20.

Step-by-step explanation:

The total amount accrued for principal plus interest in the calculation simple interest

= principal * (1+ rate * number of years)

= $800 *(1+ 6.2% * 7)

= $1,147.20.

Hopefully his helped, if not HMU and I will try my best to get u a better answer! :)

At the sewing store, Mariana bought a bag of mixed buttons. She got 80 buttons in all. 20 of the buttons were large. What percentage of the buttons were large?

Answers

Answer:

25%

Step-by-step explanation:

To find the percent of large buttons, divide the number of large buttons by the total, and divide that by 100:

(20/80) x 100

Answer:

it is 10.3

Step-by-step explanation:

In 12 hours , the temperature fell steadily from 17F to -7F. What was the change in temperature

Answers

Answer:

the change was 24F

Step-by-step explanation:

When a number x is multiplied by 6, the result is 38.

What is the value of x?

Drag and drop the correct number into the box so that the equation is true.

3/8

8/3

1/16

9/4

16

4/9

help me plz it is 10 pts

Answers

Answer:

8/3

Step-by-step explanation:

i took the quiz

Answer:

6⅓ The answer is not in the options..

Step-by-step explanation:

6x = 38

x = 38÷6

x = 6 ⅓ / 6.33333..

Kevin bought a 5 kilogram can of peanuts for 4.50. what is the unit price.

Answers

Answer:

$0.90/kg

Step-by-step explanation:

4.50/5=0.90

please help me i need this answer ASAPP!!

Answers

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[tex]y + 1 = \frac{8}{9} (x + 4) \\ [/tex]

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Thus the correct answer is the second one.

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Math question

Any complex fraction can be written as a ratio

True or False

Will give brainiest to first person to answer right

Answers

Answer:

I believe the answer is true, please let me know if I am wrong.

(n+8)+(n−12) =

what is the answer

Answers

Answer:

2n-4

Step-by-step explanation:

The value of n for the given condition is 2(n - 2).

What is simplification?

To simplify means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue. By eliminating all common factors from the numerator and denominator and putting the fraction in its simplest/lowest form, we can simplify fractions.

Given equation

(n + 8) + (n − 12) =

n + 8 + n - 12

solving constant separately and variables separately,

2n - 4

the common factor of 2 and 4 is 2

2(n - 2)

Hence the simplified form of an equation is 2(n - 2).

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The first four terms of a sequence are 16, 22, 28, 34, …
Which expression can be used to find the nth term of the sequence?

A) 6 + 10n
B)6 + 10(n - 1)
C)10 + 6(n - 1)
D)10 + 6n

Answers

Answer:

A.)

Step-by-step explanation:

I feel like it's A.) because the number sequence above continues to go on due to addition of 6 to each number. And now you are adding 6 to 10n because as stated before your supposed to add 6 to each number to get the answer in the sequence.

Hopefully I helped God bless !

у - 2x = 3
Solve for y

Answers

y - 2x = 3

Isolate y by adding 2x to both sides:

y = 3 + 2x

Answer:

y=2x+3

Step-by-step explanation:

y-2x =3

add 2x on both sides

y=2x+3

Can someone please how to do fractions in the lowest terms

Answers

Answer:

In order to out a fraction in lowest terms, you must divide by the Greatest Common Factor, or GCM, of the numerator and denominator in the fraction. Let's say we have the fraction 25/100. We know that the greastest common factor of 25 and 100 is 25, as 25 ÷ 25 = 1 and 100 ÷ 25 = 4 so 25/100 in lowest terms is 1/4:

25 25 1

___ ÷ ___ = ___

100 25 4

If the GCM of a fraction equals 1, the fraction is simplified. Because the only common factor of 1 and 4 is 1, we know this fraction is simplified.

1 1 1

__ ÷ ___ = ___

4 1 4

Hope this helps <3 Please contact me if your still confused

Scott swims several times per week in a lake near his home. Last summer, the lakes water temperature was 20 Celsius this year the average water temperature was 20% warmer what was the average temperature of the lakes this summer. Solve it step by step please

Answers

Answer:

ggggg

Step-by-step explanation:

gfv

please help me fast
I give you 100 point

Answers

do u need tbem answered?

Answer:

a. 372

b. 708

c. 451

d. 805

e. 965

f. 620

Step-by-step explanation:

Draw a model to help solve 5/6 + 1/4. write ur answer as a mixed number.

Answers

So first draw your model and add 5/6 + 1/4 and then write your answer as a mixed number

The required simplified solution of the given expression in the form of a mixed number is 1 1/12.

Given that,
To determine the solution of expression 5/6 + 1/4. in the form of a mixed number.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,

= 5 / 6 + 1 / 4
= [ 5×4 + 1×6 ] / [6×4]
= 26 / 24
= 13 / 12
= 1 + 1 /12 or 1 1/12

Thus, the required simplified solution of the given expression in the form of a mixed number is 1 1/12.

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Consider the equation 5x^2-10x+c=0. What values of c result in the equation having a complex solutions? Represent your answer on the number line

Answers

Answer:

When we have a quadratic equation:

a*x^2 + b*x + c = 0

There is something called the determinant, and this is:

D = b^2 - 4*a*c

If D < 0, then the we will have complex solutions.

In our case, we have

5*x^2 - 10*x + c = 0

Then the determinant is:

D = (-10)^2 - 4*5*c = 100 - 4*5*c

And we want this to be smaller than zero, then let's find the value of c such that the determinant is exactly zero:

D = 0 = 100 - 4*5*c

4*5*c = 100

20*c = 100

c = 100/20 = 5

As c is multiplicating the negative term in the equation, if c increases, then we will have that D < 0.

This means that c must be larger than 5 if we want to have complex solutions,

c > 5.

I can not represent this in your number line, but this would be represented with a white dot in the five, that extends infinitely to the right, something like the image below:

The equation of line CD is y = -2x - 2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4, 5).
y = -2x + 13
y=zx+7
y=x+3
y = -2x - 3

Answers

Answer:

y = -2x + 13

Step-by-step explanation:

Order all of the decimals
from least to greatest 0.34, 0.4, 0.98, 0.97, 0.46,
0.309

Answers

Answer:

.309

.34

.46

.97

.98

Step-by-step explanation:

Hope this helped. Do not be shy to give Brainlist.

Answer:

0.4, 0.309, 0.34, 0.46, 0.97, 0.98

Step-by-step explanation:

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