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3 years ago

If cot theta = -2, find the value of cot theta + cot (theta -pi) + cot (theta-2pi)

Mathematics

1 answer:

nika2105 [10]3 years ago

6 0

Given:

$\cot \theta = -2$

To find:

The value of $\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)$ .

Solution:

We know that,

$\cot (\theta -n\pi)=\cot \theta$ ...(i)

Where n is an integer.

We have,

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)$

Using (i), it can be written as

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=\cot \theta +\cot \theta +\cot \theta$

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=3\cot \theta$

It is given that $\cot \theta = -2$ .

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=3(-2)$

$\cot \theta +\cot (\theta -\pi)+\cot(\theta -2\pi)=-6$

Therefore, the value of the given function expression is $-6$ .

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The perimeter of the triangle

Illusion [34]

Area=228 feet sqa.
Length=12 ft.
Breadth=(228/12) ft.
=19 ft.
Perimeter=2(12+19) ft.
=2×31 ft.
=62 ft.

HOPE IT HELPS UH!!☺️☺️

8 0

3 years ago

What is the trigonometric ratio for cosn? enter your answer, as a simplified fraction, in the boxes. $$ triangle l m n with righ

hjlf

The trigonometric ratio will be Cos(n)=12/13

<h3>What will be the trigonometry ratio?</h3>

Given is a Right triangle LMN with right angle at M i.e. angle M = 90 degrees.

Given are the sides LM = 15, MN = 36, and LN = 39.

It says to find cos(n) = ?

So opposite side would be LM, adjacent side would be MN, and LN is the hypotenuse.

We know that the cosine ratio is given by :-

$Cos(n)=\dfrac{adjacent}{Hypotenuse}$

$Cos(n)=\dfrac{MN}{LN}$

$Cos(n)=\dfrac{36}{39}$

$Cos(n)=\dfrac{12}{13}$

Hence the required ratio will be $Cos(n)=\dfrac{12}{13}$

To know more about trigonometry, follow

trigonometry

3 0

2 years ago

A boy has only dimes and quarters in his piggy bank. if he has 70 coins worth 12 dollars and 40 cents altogether, how many quart

dlinn [17]

Let us bear in mind the equivalent value of these coins:

One dime = $0.10

One quarter = $0.25

Let x = number of dimes

y = number of quarters

Since the boy has 70 coins in total, we can say that:

x + y = 70 (can be written as x = 70 – y)

Since the boy has a total of $12.40, we can say that:

0.10x + 0.25y = 12.40

To solve this problem, we need to solve this system of equation. We have to substitute the value of x as written in the first equation (x = 70 –y)

0.10(70 – y) + 0.25y = 12.40

7 – 0.10y + 0.25y = 12.40

0.15y = 5.40

y = 36

X = 70 – 36

X = 34

Therefore, the boys has 34 dimes and 36 quarters. To check our answer, we just have to check if his money would total $12.40.

34 dimes = $3.40

36 dimes = $9.00

Total $12.40

7 0

3 years ago

Read 2 more answers

ou live in the building on the left in the drawing, and a friend lives in the other building. the two of you are having a discus

Alenkinab [10]

Answer:

1.3

Friend is wrong

Step-by-step explanation:

Given:

friend's claim: height of his building is more than 1.50 times the height of yours

line of sight to the top edge of the other building makes an angle of 21° above the horizontal

line of sight to the base of the other building makes an angle of 52° below the horizontal

Solution:

Let A be the height of your building is A

Let B+A his building is B higher than yours.

Let the distance between the buildings is x.

then

tan 52 = A/x

tan 21 = B/x

A/B = tan 52 / tan 21

= 1.27994 / 0.38386

A/B = 3.33

(A + B) / A = 1.5 0

A/A + B/A = 1.50

1 + B/A = 1.50

B/A is basically (B/x) / (A/x)

1+ 3.33 / 3.33

= 4.33/3.33

= 1.3

Since 1.3 is not equal to 1.5

Hence the friend's claim is wrong.

5 0

4 years ago

Hi i will give 50 POINTS and BRAINLIEST to whoever answers this question

Alina [70]

Answer:

$\boxed{4 : 1}$

Step-by-step explanation:

Colored Fabric = 48 mm

White Fabric = 1.2 cm

Ratio of white fabric to colored fabric is:

48 mm : 1.2 cm

To express any ratio, we need to equalize the units ( 1 cm = 10 mm)

=> 48 mm : 12 mm

÷12 ÷12

=> 4 : 1

3 0

3 years ago

Read 2 more answers