if tan theta =3, find the value of tan theta + tan (theta+pi) + tan (theta +2pi)

Answers

Answer 1

Answer:

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]

Step-by-step explanation:

Given

[tex]tan\theta = 3[/tex]

Required

Find

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex]

Calculate [tex]tan(\theta + \pi) \ and\ tan(\theta+2\pi)[/tex]

Using tan rule

[tex]tan(\theta + \pi) = \frac{tan\theta + tan\pi}{1 - tan\theta tan\pi}[/tex]

So:

[tex]tan(\theta + \pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]

[tex]tan(\theta + \pi) = \frac{tan\theta}{1 }[/tex]

[tex]tan(\theta + \pi) = \tan\theta[/tex]

[tex]tan(\theta+2\pi)[/tex]

[tex]tan(\theta + 2\pi) = \frac{tan\theta + tan2\pi}{1 - tan\theta tan2\pi}[/tex]

[tex]tan(\theta + 2\pi) = \frac{tan\theta + 0}{1 - tan\theta *0}[/tex]

[tex]tan(\theta + 2\pi) = \tan\theta[/tex]'

'So:

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi)[/tex] [tex]= tan\theta +tan\theta +tan\theta[/tex]

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 3+3+3[/tex]

[tex]tan\theta + tan(\theta + \pi) + tan(\theta+2\pi) = 9[/tex]


Related Questions

What does 3 to the power of 2 minus 4 times 2 plus 6

Answers

Answer:

7 is the answer

Step-by-step explanation:

Answer:

This equals 7

Step-by-step explanation:

I used a calculator

Can I have brainliest pls

Identify each pair of angles as corresponding, Alternate interior, alternate exterior, or consecutive interior and solve for X

Answers

Answer:

Step-by-step explanation:

19). Angles measuring 90° and (21x + 6)° are Alternate exterior angles.

     Therefore, 21x + 6 = 90

     2x = 90 - 6

     2x = 84

      x = 42

21). Angles measuring 60° and (8x - 4)° are Alternate interior angles,

      8x - 4 = 60

      8x = 60 + 4

      x = [tex]\frac{64}{8}[/tex]

      x = 8

23). Since, angles measuring (-1 + 14x)° and (12x + 17)° are Alternate exterior angles

    Therefore, (-1 + 14x) = (12x + 17)

     14x - 12x = 17 + 1

     2x = 18

      x = 9

25). Both the angles (x + 96)° and (x + 96)° are consecutive interior angles.

      Therefore, (x + 96)° + (x + 96)° = 180° [Property of consecutive interior angles]

      2x + 192 = 180

      2x = 180 - 192

      2x = -12

       x = -6

       Now measure of (x + 96)° = -6 + 96

                                                = 90°

26). Both the angles (20x + 5)° and (24x - 1)° are consecutive interior angles.

      Therefore, (20x + 5)° + (24x - 1)° = 180°

       44x + 4 = 180

       44x = 176

        x = 4

There are 20 pieces of fruit in a basket and 12 of them are oranges. What percentage of the pieces of fruit in the basket are oranges? Show your work in the box and circle your answer

Answers

Answer:60 percent

Step-by-step explanation: You have fraction the two numbers which will be 12/20 them you times it by 100 which equals 60 oranges.

if f(x)=5x-7,what isf(3)?​

Answers

Answer:

Explanation:

f  (  − 3 )  basically means substitute  − 3  for  x  in the function  − 5 x

f

(

3

)

=

5

(

3

)

7

f

(

3

)

=

15

7

f

(

3

)

=8

Step-by-step explanation:

Need the answer ASAP

Answers

Answer:

63

Step-by-step explanation:

To find the area of a trapezoid you have to use the formula

a+b/2 h

So we would substitute them

3 + 15 / 2 x 7

Which would equal

63

Hope this helps :)

Investigate the patern “13/1 family” of fractions. Use plenty of space to show what you find.

Answers

Answer:

2/1 of a family

Step-by-step explanation:

find the length of AD. HELP MEEEE​

Answers

Answer:

5.42

Step-by-step explanation:

hope this helped!! :)

1) Find the missing angle.
31°
949

Answers

? + 31° + 94° = 180°

? + 125° = 180°

? = 180° - 125°

? = 55°

Answer: 52°

Step-by-step explanation:

Angles in a triangle always add up to 180°.

So to work out what the missing angle is, you would have to add 34 and 94 together.

34+94=128

Then you would have to take 128 away from 180.

180-128=52°

Hope this helps :)

PLEASE HELP ME........​

Answers

Answer:

d

Step-by-step explanation:

can someone help having trouble solving this question

Answers

Answer:

if you pit the shape in a straight line it would be 180 degrees now take 180 take 130 and 100 and subtract those add that to the other 30 then take 180 divided by 60

Answer:

x = 50°

Step-by-step explanation:

sum of exterior angles is always equal to 360°

so, we can add all the given numbers and set them equal to 360° to find x:

130° + 30° + 100° + x° + x° = 360°

260° + 2x = 360°

2x = 100°

x = 50°

Please help- will give brainlist

Answers

Answer:

m(JCA)

Step-by-step explanation:

C is the central angle here (the one in between)

so it will be m(JCA) or m(ACJ)

Gibson (1986) asked a sample of college students to complete a self-esteem scale on which the midpoint of the scale was the score 108. He found that the average self-esteem score for this sample was 135.2, well above the actual midpoint of the scale. Given that the standard deviation of self-esteem scores was 28.15, what would the z score be for a person whose self-esteem score was 101.6

Answers

Answer:

The z-score for a person whose self-esteem score was 101.6 would be of -0.227.

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Gibson (1986) asked a sample of college students to complete a self-esteem scale on which the midpoint of the scale was the score 108.

This means that [tex]\mu = 108[/tex]

The standard deviation of self-esteem scores was 28.15

This means that [tex]\sigma = 28.15[/tex]

What would the z score be for a person whose self-esteem score was 101.6

This is Z when X = 101.6. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{101.6 - 108}{28.15}[/tex]

[tex]Z = -0.227[/tex]

The z-score for a person whose self-esteem score was 101.6 would be of -0.227.

(Urgent) Worth 15 points 7.3

Answers

Answer: 20790

Step-by-step explanation:

5x-3 < 22 help plssssss

Answers

Answer: x=25/5

Step-by-step explanation:

Answer:

x<5

Step-by-step explanation:

add 3 to both sides to get 5x alone

so 5x<25, divide by 5 to get x alone

1) John is a mountaineer. He went on a long hike. He
started his bike at 250 feet above sea level. When he
reached the peak of the mountain, he was at
1,500 feet above sea level. How many feet did
John hike up the mountain?

Answers

Answer:

1,250 feet.

Step-by-step explanation:

1500-250=1250

Julie's grades for this term test are 85,88,97. What is her average?
Please give an explanation.

Answers

Answer:

90

Step-by-step explanation:

The average of a set of numbers is the sum of the numbers, divided by the count of the numbers.

Thus, the average of 85, 88 and 97 is

85 + 88 + 97

------------------- = 270/3, or 90

         3

Answer:

90

Step-by-step explanation:

The radius of a circle is 3.9 in. Find the circumference to the nearest tenth.​

Answers

Answer:

24.5

Step-by-step explanation:

please OMG I DONT UNDERSTAND

Answers

Answer:

ANSWER

Step-by-step explanation:

Umaloja vendeu 2.800 calçado no mês passado, neste mês vendeu10% a mais. Quantos calçados foram ven- didos neste mês​

Answers

Answer:

3.080 calzados.

Step-by-step explanation:

Dado que Umaloja vendió 2.800 calzados el mes pasado, y este mes vendió un 10% más, para determinar cuantos calzados fueron vendidos este mes se debe realizar el siguiente cálculo:

2800 + ((2.800 x 10) / 100) = X

2.800 + (28.000 / 100) = X

2.800 + 280 = X

3.080 = X

Así, este mes Umaloja vendió 3.080 calzados.

Find the area of the shape shown below.

Answers

Answer: 4, 800

Step-by-step explanation:

The length of a rectangle is x feet more than its width. The area of the rectangle is 5x + 25. What is the width of the rectangle?

Answers

Answer:

w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

Before we start the solving, we can make the following statements:

Area = l x w

Area = 5x + 25

therefore,

l x w = 5x + 25

Since the question states that the length is x more than the width, so we can make the following statement:

w = l + x

With this, we can substitute it to the first statement we made, l x w = 5x + 25,

l x (l + x) = 5x + 25

[tex]l^{2}[/tex] + lx = 5x + 25

lx - 5x = 25 - [tex]l^{2}[/tex]

x(l - 5) = 25 - [tex]l^{2}[/tex]

x = [tex]\frac{25 - l^{2}}{l - 5}[/tex]

From this, we can find w by substituting it in the statement we made earlier, w = l + x,

w = [tex]l + \frac{25 - l^{2}}{l - 5}[/tex]

Use similar triangles to solve for the missing lengths below.

If you know how to work this out please help:)

Answers

Answer:

x = 14

y = 18

Step-by-step explanation:

By the property of similar triangles,

If two triangles are similar their corresponding sides will be proportional.

[tex]\frac{AB}{EF}= \frac{AC}{GE}[/tex]

[tex]\frac{5}{10}=\frac{7}{x}[/tex]

x = [tex]\frac{70}{5}[/tex]

x = 14

Similarly, [tex]\frac{AB}{EF}= \frac{CB}{GF}[/tex]

[tex]\frac{5}{10}=\frac{9}{y}[/tex]

y = [tex]\frac{90}{5}[/tex]

y = 18

Which transformation could NOT be used to prove that two circles are congruent to one another?

Answers

Answer: D

Step-by-step explanation:

Helps, is it 64 111 or 90?​

Answers

Answer:

111

Step-by-step explanation:

Find X please help me with test corrections due midnight tonight!
If HBN is congruent to LYR.

Answers

Answer:

the answer is

x=22..........

what is the slope of the line passing through the points (4,7) and (-2,10)?

Answers

Answer:

-1/2

Step-by-step explanation:

Answer:

the answer is the slope is -1/2

there are 144 microscopes in boxes at a school. each box has 24 microscopes which equation could be used to find b, the number of boxes of microscopes at this school

A. 24+144= b
B. 144-b= 24
C. B divided by 24= 144
D. 24 x b= 144

Answers

D ...................

Which expression is equivalent to sqrt -108 - sqrt -3?

A) 5 sqrt 3i
B) 6 sqrt 3i
C) 7 sqrt 3i
D) 8 sqrt 3i

Answers

Answer is c) 7sqrt 3i

The logarithm of a number to the base V2 is k. What is its logarithm to the base 2v2 ?​

Answers

Answer:

[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]

Step-by-step explanation:

Given

Let the number be X

From the first statement, we have:

[tex]log_{\sqrt 2} X = k[/tex]

Required

Find [tex]log_{2\sqrt 2} X[/tex]

[tex]log_{\sqrt 2} X = k[/tex]

using the following law of logarithm

[tex]log_ab = n, b=a^n[/tex]

So:

[tex]log_{\sqrt 2} X = k[/tex]

[tex]X = \sqrt{2}^k[/tex]

Substitute: [tex]X = \sqrt{2}^k[/tex] in [tex]log_{2\sqrt 2} X[/tex]

[tex]log_{2\sqrt 2} X = log_{2\sqrt 2} ( \sqrt{2}^k)[/tex]

[tex]log_{2\sqrt 2} X = klog_{2\sqrt 2} \sqrt{2}[/tex]

Apply the following law:

[tex]log_ab = \frac{log\ b}{log\ a}[/tex]

[tex]log_{2\sqrt 2} X = k\frac{log\ \sqrt 2}{log\ {2\sqrt 2}}[/tex]

Express the square roots as power

[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2 * 2^\frac{1}{2}}}[/tex]

[tex]log_{2\sqrt 2} X = k\frac{log\ 2^\frac{1}{2}}{log\ {2^\frac{3}{2}}}[/tex]

using the following law of logarithm

[tex]log_ab = n, b=a^n[/tex]

[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}log\ 2}{\frac{3}{2}log\ 2}}[/tex]

[tex]log_{2\sqrt 2} X = k\frac{\frac{1}{2}}{\frac{3}{2}}}[/tex]

Rewrite as:

[tex]log_{2\sqrt 2} X = k * \frac{1}{2} \div\frac{3}{2}[/tex]

[tex]log_{2\sqrt 2} X = k * \frac{1}{2} *\frac{2}{3}[/tex]

[tex]log_{2\sqrt 2} X = k * \frac{1}{1} *\frac{1}{3}[/tex]

[tex]log_{2\sqrt 2} X = \frac{1}{3}k[/tex]

use the graph below to write the equation of the function

Answers

Answer:

c

Step-by-step explanation:

gefhhfeyjhtwgi15287

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