Math / Trigonometry

QuestionA point is given in polar coordinates. Convert the point to rectangular coordinates. $(x, y)=(\square)$

Studdy Solution

STEP 1

1. The point is given in polar coordinates as $(r, \theta) = (0, -7\pi)$ .
2. The conversion from polar to rectangular coordinates uses the formulas $x = r \cos \theta$ and $y = r \sin \theta$ .

STEP 2

1. Identify the given polar coordinates.
2. Apply the conversion formulas to find $x$ .
3. Apply the conversion formulas to find $y$ .
4. Write the rectangular coordinates.

STEP 3

Identify the given polar coordinates:
Given $r = 0$ and $\theta = -7\pi$ .

STEP 4

Apply the conversion formula for $x$ :
$x = r \cos \theta$ $x = 0 \cdot \cos(-7\pi)$
Since $r = 0$ , it follows that:
$x = 0$

STEP 5

Apply the conversion formula for $y$ :
$y = r \sin \theta$ $y = 0 \cdot \sin(-7\pi)$
Since $r = 0$ , it follows that:
$y = 0$

STEP 6

Write the rectangular coordinates:
The rectangular coordinates are $(x, y) = (0, 0)$ .
The rectangular coordinates are:
$\boxed{(0, 0)}$

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QuestionA point is given in polar coordinates. Convert the point to rectangular coordinates. $(x, y)=(\square)$

Studdy Solution

STEP 1

1. The point is given in polar coordinates as $(r, \theta) = (0, -7\pi)$ .
2. The conversion from polar to rectangular coordinates uses the formulas $x = r \cos \theta$ and $y = r \sin \theta$ .

STEP 2

1. Identify the given polar coordinates.
2. Apply the conversion formulas to find $x$ .
3. Apply the conversion formulas to find $y$ .
4. Write the rectangular coordinates.

STEP 3

Identify the given polar coordinates:
Given $r = 0$ and $\theta = -7\pi$ .

STEP 4

Apply the conversion formula for $x$ :
$x = r \cos \theta$ $x = 0 \cdot \cos(-7\pi)$
Since $r = 0$ , it follows that:
$x = 0$

STEP 5

Apply the conversion formula for $y$ :
$y = r \sin \theta$ $y = 0 \cdot \sin(-7\pi)$
Since $r = 0$ , it follows that:
$y = 0$

STEP 6

Write the rectangular coordinates:
The rectangular coordinates are $(x, y) = (0, 0)$ .
The rectangular coordinates are:
$\boxed{(0, 0)}$

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QuestionA point is given in polar coordinates. Convert the point to rectangular coordinates. (x,y)=(□)(x, y)=(\square)(x,y)=(□)

Studdy Solution

STEP 1

1. The point is given in polar coordinates as (r,θ)=(0,−7π)(r, \theta) = (0, -7\pi)(r,θ)=(0,−7π).2. The conversion from polar to rectangular coordinates uses the formulas x=rcos⁡θx = r \cos \thetax=rcosθ and y=rsin⁡θy = r \sin \thetay=rsinθ.

STEP 2

1. Identify the given polar coordinates.2. Apply the conversion formulas to find xxx.3. Apply the conversion formulas to find yyy.4. Write the rectangular coordinates.

STEP 3

Identify the given polar coordinates:Given r=0r = 0r=0 and θ=−7π\theta = -7\piθ=−7π.

STEP 4

Apply the conversion formula for xxx:x=rcos⁡θ x = r \cos \theta x=rcosθ x=0⋅cos⁡(−7π) x = 0 \cdot \cos(-7\pi) x=0⋅cos(−7π)Since r=0r = 0r=0, it follows that:x=0 x = 0 x=0

STEP 5

Apply the conversion formula for yyy:y=rsin⁡θ y = r \sin \theta y=rsinθ y=0⋅sin⁡(−7π) y = 0 \cdot \sin(-7\pi) y=0⋅sin(−7π)Since r=0r = 0r=0, it follows that:y=0 y = 0 y=0

STEP 6

Write the rectangular coordinates:The rectangular coordinates are (x,y)=(0,0)(x, y) = (0, 0)(x,y)=(0,0). The rectangular coordinates are:(0,0) \boxed{(0, 0)} (0,0)​

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QuestionA point is given in polar coordinates. Convert the point to rectangular coordinates. $(x, y)=(\square)$

1. The point is given in polar coordinates as $(r, \theta) = (0, -7\pi)$ .
2. The conversion from polar to rectangular coordinates uses the formulas $x = r \cos \theta$ and $y = r \sin \theta$ .

1. Identify the given polar coordinates.
2. Apply the conversion formulas to find $x$ .
3. Apply the conversion formulas to find $y$ .
4. Write the rectangular coordinates.

Identify the given polar coordinates:
Given $r = 0$ and $\theta = -7\pi$ .

Apply the conversion formula for $x$ :
$x = r \cos \theta$ $x = 0 \cdot \cos(-7\pi)$
Since $r = 0$ , it follows that:
$x = 0$

Apply the conversion formula for $y$ :
$y = r \sin \theta$ $y = 0 \cdot \sin(-7\pi)$
Since $r = 0$ , it follows that:
$y = 0$

Write the rectangular coordinates:
The rectangular coordinates are $(x, y) = (0, 0)$ .
The rectangular coordinates are:
$\boxed{(0, 0)}$