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Rudiy27
2 years ago
13

Convert the polar coordinates (-3, -60°) to Cartesian coordinates.

Mathematics
1 answer:
notsponge [240]2 years ago
6 0

Answer:

(1.5,-2.6)

Step-by-step explanation:

Given the polar coordinates (-3,60°).

Let our Cartesian coordinates be (x,y)

#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:

r=\sqrt{x^2+y^2}\\\\\therefore r^2=x^2+y^2\\\\\theta=tan^{-1}(y/x)\\\therefore tan \theta=y/x

#Using the illustration above, we can express our polar coordinates as:

-3=\sqrt{x^2+y^2}\\\\-60\textdegree=tan^{-1}(y/x}

#Solve simultaneously to solve for x and y:

(-3)^2=x^2+y^2\ \ \ \ \ \ \ \ \ \ i\\\\tan(-0\texdegree)=y/x\ \ \ \ \ \ \ \ ...ii\\\\y=x\ tan(-60\textdegree)\ \ \ \ \ \ \ ...iii\\\\\#substitute\  y \ in\  i\\\\(-3)^2=x^2+(x \ tan (-60\textdegree))^2\\\\9=x^2+3x^2\\\\x=\sqrt{9/4}=1.5\\\\y=1.5\ tan(-60\textdegree)=-2.5981\approx-2.6

Hence, the Cartesian coordinates are (1.5,-2.6)

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s2008m [1.1K]

y=5x^2+7 is Non-Linear Functions

Option B is correct option.

Step-by-step explanation:

We need to identify Non-Linear Functions from the equations given.

First we will define Non-Linear Functions

<u>Linear Functions</u>

A function having exponent of variable equal to 1 or of the form y=c, where c is constant is called linear function.

<u>Non-Linear Functions</u>

A function that has variable having power greater than 1 (i.e 2 or above) is called non-linear function.

So, from all the options given, only Option B has power greater than 1 i.e 2. All remaining options are linear functions.

So, y=5x^2+7 is Non-Linear Functions

Option B is correct option.

Keywords: Linear and Non-Linear Functions

Learn more about Linear and Non-linear functions at:

  • brainly.com/question/12363217
  • brainly.com/question/4326955

#learnwithBrainly

3 0
2 years ago
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IRISSAK [1]
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3 years ago
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nexus9112 [7]

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Step-by-step explanation:

hope this helps :)

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6 0
2 years ago
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