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makvit [3.9K]
3 years ago
5

What is cos(45°)?

Mathematics
1 answer:
Andrej [43]3 years ago
6 0

Answer:

\rm \dfrac{\sqrt2}{2}

Step-by-step explanation:

A right angled ∆ is given to us and we need to find out the value of cos 45° ( with rationalized denominator ) . As we know that in a right angle ∆ , the value of cosine is ,

\rm\implies cos\theta =\dfrac{base}{hypotenuse}

In the given triangle ,

  • Value of base = 1
  • Value of hypotenuse = √2

On substituting the respective values ,

\rm\implies cos45^\circ =\dfrac{1}{\sqrt2}

For rationalizing the denominator , multiply numerator and denominator by √2 , we have,

\rm\implies cos45^\circ=\dfrac{1(\sqrt2)}{(\sqrt2)(\sqrt2)}

Simplify ,

\rm\implies \boxed{\pink{\frak{ cos45^\circ=\dfrac{\sqrt2}{2} }}}

You might be interested in
∠A and \angle B∠B are supplementary angles. If m\angle A=(2x-16)^{\circ}∠A=(2x−16) ∘ and m\angle B=(5x+28)^{\circ}∠B=(5x+28) ∘ ,
Otrada [13]

Answer:

The measure of angle A is 32

Step-by-step explanation:

A+B=180

2x-16+5x+28=180

7x+12=180

7x=168

x=24

A=2(24)-16

A=48-16

A=32

6 0
3 years ago
Solve the equation. |x + 5| = 9 {–4, 14} {–14, 4} {4, 14} {–14, –4}
inna [77]

Answer:

{-14, 4}

Step-by-step explanation:

the absolute value function only makes sure that the result always has a positive sign.

so, (x + 5) must be either +9 or -9 to make the original equation true. the absolute value would turn both into +9.

so,

x + 5 = 9

x = 4

and

x + 5 = -9

x = -14

that gives us the correct set of solutions as indicated above.

6 0
2 years ago
A go-cart with a mass of 200 kg is pushed with a force of 1000 N (1000 kg m/s2). What is the acceleration of the go-cart? ​
Hunter-Best [27]

Answer:

Acceleration=5m/s^2

Step-by-step explanation:

F=ma

1000=200xa

a=1000/200

a=5m/s^2

8 0
3 years ago
Write as a product:<br> a2+b2–2ab –25
kozerog [31]

Answer:  -a2 - 2ab - b2 + 25  =

 -1 • (a2 + 2ab + b2 - 25)

Final result :

 -a2 - 2ab - b2 + 25

Step-by-step explanation:

3 0
3 years ago
In 2013, the population of China was estimated to be 1,360,760,100. Round off the number of people 
Aleksandr [31]

Answer:

a) 1,360,760,000

b) 1,361,000,000

c) 1,400,000,000

d)  1,360,800,000

Step-by-step explanation:

We have to round off the given population number to certain digits.

The following are the rules to round of a number:

  1. First identify the digit to be rounded.
  2. If this digit is followed by 5,6,7,8,9 then we round up the number that is increase the digit by 1 and all the numbers to right becomes zero.
  3. If this digit is followed by 0,1,2,3,4 then we round down the number that is decrease the digit by 1 and all the numbers to right becomes zero.

a)  to the nearest thousand.

Thousands place: 0

Right Digit: 1

We round down the number

Rounded to the nearest 1,000 or t he thousands Place =  1,360,760,000

b)  to the nearest million

Millions place: 0

Right Digit: 7

We round up the number

Rounded to the nearest million places = 1,361,000,000

c)  to nearest hundred million

Hundred million place: 3

Right Digit: 6

We round up the number

Rounded to the nearest million places = 1,400,000,000

d)  to the nearest hundred thousand.

hundred thousand place: 7

Right Digit: 6

We round up the number

Rounded to the nearest million places = 1,360,800,000

7 0
3 years ago
Read 2 more answers
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