Solve the trigonometric equation over the interval [0, 2) [tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]Show your work, thanks!

Answer: = 0 , 60Step-by-step explanation:[tex]\cos^2\theta + \sqrt{3}\sin \theta \cos \theta = 1[/tex]Substract both the sides from 1.[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 1 - 1[/tex][tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 0[/tex]Rearrange the terms in L.H.S. [tex]=> (\cos^2 \theta - 1 )+ \sqrt{3} \sin \theta \cos \theta = 0[/tex]Replace the terms in brackets with '-sin' by using the identity (sin + cos = 1).[tex]=> -\sin^2 \theta + \sqrt{3} \sin \theta \cos \theta = 0[/tex]Take 'sin' common from the whole expression in L.H.S.[tex]=> \sin \theta(- \sin \theta + \sqrt{3}\cos \theta) = 0[/tex]Now solve each part separately :-1) [tex]\sin \theta = 0[/tex][tex]=> \theta = \sin^{-1}0 = 0[/tex]2) [tex]-\sin \theta + \sqrt{3} \cos \theta = 0[/tex]Divide both the sides by 'cos'.[tex]=> \frac{-\sin \theta + \sqrt{3}\cos \theta }{\cos \theta} = \frac{0}{\cos \theta}[/tex][tex]=> \frac{-sin \theta}{\cos \theta} + \frac{\sqrt{3} \cos \theta}{\cos \theta} = 0[/tex][tex]=> -\tan \theta + \sqrt{3} = 0[/tex]Add both the sides with 'tan'.[tex]=> -\tan \theta + \sqrt{3} + \tan \theta = 0 + \tan \theta[/tex][tex]=> \tan \theta = \sqrt{3}[/tex][tex]=> \theta = \tan^{-1}\sqrt{3} = 60[/tex] = 0 , 60

Mathematics High School

Solve the trigonometric equation over the interval [0, 2π)
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
Show your work, thanks!

Answers

Answer 1

Answer:

θ = 0° , 60°

Step-by-step explanation:

[tex]\cos^2\theta + \sqrt{3}\sin \theta \cos \theta = 1[/tex]

Substract both the sides from 1.

[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 1 - 1[/tex]

[tex]=> \cos^2\theta + \sqrt{3}\sin \theta \cos \theta - 1 = 0[/tex]

Rearrange the terms in L.H.S.

[tex]=> (\cos^2 \theta - 1 )+ \sqrt{3} \sin \theta \cos \theta = 0[/tex]

Replace the terms in brackets with '-sin²θ' by using the identity (sin²θ + cos²θ = 1).

[tex]=> -\sin^2 \theta + \sqrt{3} \sin \theta \cos \theta = 0[/tex]

Take 'sinθ' common from the whole expression in L.H.S.

[tex]=> \sin \theta(- \sin \theta + \sqrt{3}\cos \theta) = 0[/tex]

Now solve each part separately :-

1) [tex]\sin \theta = 0[/tex]

[tex]=> \theta = \sin^{-1}0 = 0[/tex]

2) [tex]-\sin \theta + \sqrt{3} \cos \theta = 0[/tex]

Divide both the sides by 'cosθ'.

[tex]=> \frac{-\sin \theta + \sqrt{3}\cos \theta }{\cos \theta} = \frac{0}{\cos \theta}[/tex]

[tex]=> \frac{-sin \theta}{\cos \theta} + \frac{\sqrt{3} \cos \theta}{\cos \theta} = 0[/tex]

[tex]=> -\tan \theta + \sqrt{3} = 0[/tex]

Add both the sides with 'tanθ'.

[tex]=> -\tan \theta + \sqrt{3} + \tan \theta = 0 + \tan \theta[/tex]

[tex]=> \tan \theta = \sqrt{3}[/tex]

[tex]=> \theta = \tan^{-1}\sqrt{3} = 60[/tex]

∴ θ = 0° , 60°

Answer 2

Answer:

Solution given:

[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]

[tex] 1-sin^{2} \theta+\sqrt{3} sin \theta cos \theta = 1[/tex]

[tex] 1-1 +sin^{2}\theta=\sqrt{3} sin \theta cos \theta = 1[/tex]

[tex] Sin\theta(sin\theta -\sqrt{3}cos\theta)[/tex]

Either

[tex] sin\theta=\sqrt{3} cos \theta [/tex]

[tex] \sqrt{sin\theta}{cos \theta}=\sqrt{3} [/tex]

[tex] Tan \theta =\sqrt{3}[/tex]

[tex] Tan \theta =Tan 60,Tan(180+60),Tan (360+60)[/tex]

[tex] \theta =60°,240°,420°[/tex]

in terms of π is

[tex] \theta =⅓π,\frac{4}{3}π,[/tex]

[tex] Sin\theta=1[/tex]

[tex]Sin\theta=Sin0° ,Sin180°[/tex]

In terms of π is

[tex]\theta=0π,π[/tex]

[tex]\theta=0π,⅓π,π,\frac{4}{3}π,[/tex]

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Answers

Answer:

The answer is 32 I just know it

The transportation department predicts that about 800,000 cars will be registered in a certain state by year 2012. Their license plates are made using and two letters followed by and three digits from 0 to 9. Will there be enough possible arrangements?

Answers

Answer:

There won't be enough arrangement

Step-by-step explanation:

Given

[tex]Letters = 2[/tex]

[tex]Digits= 3[/tex]

[tex]Cars = 800000[/tex]

Required

Determine if the possible arrangement will be enough

The 2 letters can be selected from any of the 26 alphabets without restriction.

So, the selection of letters is:

[tex]Letters = 26 * 26[/tex]

The 3 digits can be selected from any of the 10 digits without restriction.

So, the selection of digits is:

[tex]Digits = 10*10*10[/tex]

The total arrangement is:

[tex]Total = Letters * Digits[/tex]

[tex]Total = 26*26*10*10*10[/tex]

[tex]Total = 676000[/tex]

By comparison:

[tex]Total < Cars[/tex]

i.e.

[tex]676000 < 800000[/tex]

Hence, the arrangement will not be enough

5. How many 1/2 cups can be filled with 500 milliliters of liquid?

Answers

Answer:

1/2 = 120ml

Step-by-step explanation:

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Find the RATIO and the EXACT VALUE of the given Sec A.

Answers

Answer:

Step-by-step explanation:

take angle A as reference angle

using sec rule

sec A=hypotenuse/adjacent

sec A=13/5

sec A=2.6

A=68 degree

for ratio,

sec A=13/5

the answer is 13/5

expiation:

What does this mean and what is the answer?

-3(-7)

Answers

Answer:

-3 * -7 = 21

Step-by-step explanation:

-3(-7) = -3 * -7

Multiply

Remember: negative * negative = positive

So -3*-7 = 21

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

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Over time, the function is DECREASING. Cho ran at a faster rate during segment K.

Step-by-step explanation:

Decreasing during segment K

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Answer:

All beside D

Step-by-step explanation:

If Jayna's shuffler is working properly and randomizing the playlist after each song, what is the probability of playing a slow song?

ANSWER IS 33.33%

Answers

Answer:

1 song is a slow song, 2 songs are not

Step-by-step explanation:

that would give you 1/3 probability = 33.3333333333333%

Dose anyone know how to solve this?

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Answer:

Domain = [-5, -2) U (1, 3)

Range = (-3, 4]

Step-by-step explanation:

Domain is the x values

Domain = [-5, -2) U (1, 3)

Range is the y values

Range = (-3, 4]

convert 8m 32 cm into centimeters

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Answer:

832 cm one meter us equal to 100 cm so 8 multiply 100 plus 32 is equal to 832

f , what is the truncation error for S3?

0.016
0.031
0.219
0.234

Answers

Answer: it’s B, 0.031

Step-by-step explanation: edge 2021

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Answer:

if there smaller than 90 degrees then it's acute if the angle is bigger then 90 degrees it's obtuse

Step-by-step explanation:

What is the next number in the pattern below? 6, 13, 21, 30, ____

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Answer:

Step-by-step explanation:

6+7=13

13+8=21

21+9=30

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2x-y=10 y=-4x+2 substitution method

Answers

Answer:

the solution is (2, -6)

Step-by-step explanation:

Substitute the second equation into the first, replacing y in the first:

2x - (-4x+2) = 10

Simplifying, we get:

2x + 4x - 2 = 10, or:

6x = 12, which yields x = 2.

Substituting 2 for x in the second equation yields y = -4(2) + 2 = 0, or y = -6

Then the solution is (2, -6).

The ratio of the measurement of an angle to its complement is 1: 2. Find the measurement of the angle and it’s complement.

Answers

Answer:

1.x=90 degrees

2.smaller angles =30

3.larger angles =(30×2)=60

Step-by-step explanation:

Complement angle=90 degrees

90/3 (because need to separate into 3 parts) =30 degrees

1part =30 degrees

1:2

(1×30):(2×30)

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Mr. Carr is hiring a plumber to repair his sink. The cost of Plumber T is shown in the table.

A table titled Plumber T Costs is shown. It has three columns and two rows. Row one is labeled Hours, h. Row two is labeled Cost, c. One hour, one hundred twenty-eight dollars. Two hours, two hundred fifteen dollars. Three hours, three hundred two dollars.

Part A. What is the initial cost and hourly rate of Plumber T?

Part B. Write an equation to represent the function shown in the table.

Part C. Plumber W charges $95 per hour and an additional $32 for the parts needed. What is the difference in cost between Plumber W and Plumber T if the repair Mr. Carr needs takes 5 hours?

Enter the correct answers in the boxes.

A. Initial cost: $

Rate per hour: $

B. Equation:

C. Difference in cost: $

Answers

The hourly rate of plumber T is $87 per hour and have an initial cost of $41.

Linear equation

Linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial amount.

From the table, using points (1, 128) and (2, 215):

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-128=\frac{215-128}{2-1}(x-1)\\ \\y= 87x+41[/tex]

The hourly rate of plumber T is $87 per hour and have an initial cost of $41.

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Answer:

Initial cost: $ 41

Rate per hour: $87

Equation: y=87x+41

Step-by-step explanation:

Sorry I do not know the difference in cost.

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Answer:

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Step-by-step explanation:

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what does the following expression mean?
7!

A. 7+6+5+4+3+2+1
B. 7·6·5·4·3·2·1

Answers

Answer: B

Step-by-step explanation:

A factorial is multiplying the integer and all of the integers below it together.

The product of a whole number 'n' with every whole number until 1 is called the factorial. The correct option is B.

What is a factorial?

The product of a whole number 'n' with every whole number until 1 is called the factorial. The factorial of 4 is, for example, 43221, which equals 24.

The expression 7! means 7 factorial which is expanded as,

7! = 7 × 6 × 5 × 4 × 3 × 2 × 1

Hence, the correct option is B.

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Solve the trigonometric equation over the interval [0, 2π) [tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]Show your work, thanks!​

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Solve the trigonometric equation over the interval [0, 2π)
[tex] \large{ {cos}^{2} \theta + \sqrt{3} sin \theta cos \theta = 1}[/tex]
Show your work, thanks!