1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tanzania [10]
3 years ago
13

Please help and thank you!

Mathematics
1 answer:
Lynna [10]3 years ago
6 0

Since polar coordinates are made up in this way

(r, \theta )

we need to solve for r and then find the angle. In our rectangular coordinate given,

(-4,-4\sqrt{3})

x = -4 and y=-4\sqrt{3}

We will use this fact to first find the angle then r, which might seem backwards but I am going to do it in this order. The formula to find the angle measure uses the tangent identity

tan\theta=\frac{y}{x}.

Filling in our y and x from the rectangular coordinate we have

tan\theta=\frac{-4\sqrt{3}}{-4} or

tan\theta =\frac{\sqrt{3}}{1}.

The tangent identity is the side opposite the reference angle (theta) over the side adjacent to it. Since in our rectangular coordinate both x and y are negative, we will be in QIII where x and y are negative. The side across from the reference angle is the square root of 3, which should tell us at this point in our math careers that the reference angle is a 60 degree angle. But in the third quadrant, the angle is 180+60 which is 240 degrees. Converting that to radians we get \frac{4\pi}{3}. That's our angle. In order to solve for r now, we will need the cosine of that angle. In our 30-60-90 right triangle we can solve for the length of the missing side which is the hypotenuse. If our Pythagorean triple is

(x, x\sqrt{3},2x)

and x = -4, then the length of the hypotenuse is 2(-4) which is -8 but since a hypotenuse is never negative, it's just 8. That's also the value for r! That means that the polar coordinates that are the same as the rectangular ones we were given are

(8,\frac{4\pi}{3})

first choice above.

You might be interested in
Help me with this!!!!
Lelechka [254]

Answer:

You didn't show the whole question.

Step-by-step explanation:

4 0
2 years ago
Rachel is now 11 years old. Five years ago, Lily was twice as old as Rachel. How old is Lily now?
Deffense [45]
Since five years ago rachel was 6, that makes lily 12 years old. that was five years ago so 12 + 5 = 17. Lily is now 17 years old.
3 0
2 years ago
A food corner in disney spring has been selling 7000 hot dogs per week,
Bad White [126]

is it 10000

if this is wrong sorry

3 0
2 years ago
Could any one help me.
shtirl [24]
I got u! (numerator)/(denominator)
* ^2 : squared
*^3 : cubed
1a) (5x^2-11x-9)/(x^2+5x-24)
1b) (-4x^2-6x-6)/(x^3+x^2-9x-9)
1c) (16x^3)/(y^2)
1d) (1)/(x+3^2)
7 0
2 years ago
High Street dog 28 of your muffins that was 7 out of 10 of all of them how many are left
velikii [3]
12 muffins are left.
8 0
3 years ago
Other questions:
  • Round 13.045 to the nearest whole number.
    12·2 answers
  • Leala took five tests in science. Find her average score to the nearest tenth:
    9·2 answers
  • Make up a story that can be represented by y=4x
    15·1 answer
  • Help! Please write the coordinates
    8·1 answer
  • What element is found more in complex carbohydrates than in simple carbohydrates?
    14·1 answer
  • Samantha reports that 60% of the first year students at her university think they should be able to bring a car to campus. She a
    5·1 answer
  • f as a function of x is equal to the square root of quantity x plus six; g(x) = 8x - 10 Find f(g(x)).
    14·1 answer
  • The total distance jim traveled on his bicycle during a 5 hour period is shown in the graph below.
    12·1 answer
  • Entos,
    6·1 answer
  • What is the solution to the system of equations?
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!