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High School Math : Understanding Polar Coordinates

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Example Questions

Example Question #1 : Calculus Ii — Integrals

The polar coordinates of a point are $\left(2.1, \frac{7\pi }{3}\right )$ $\displaystyle \left(2.1, \frac{7\pi }{3}\right )$. Give its $\displaystyle y$-coordinate in the rectangular coordinate system (nearest hundredth).

Possible Answers:

4.20 $\displaystyle 4.20$

1.82 $\displaystyle 1.82$

1.05 $\displaystyle 1.05$

-1.05 $\displaystyle -1.05$

-1.82 $\displaystyle -1.82$

Correct answer:

1.82 $\displaystyle 1.82$

Explanation:

Given the polar coordinates $(r,\theta )$ $\displaystyle (r,\theta )$, the $\displaystyle y$-coordinate is $y= r \sin \theta$ $\displaystyle y= r \sin \theta$. We can find this coordinate by substituting $r = 2.1, \theta = \frac{7\pi }{3}$ $\displaystyle r = 2.1, \theta = \frac{7\pi }{3}$:

$y = r \sin \theta = 2.1 \cdot \sin \frac{7\pi }{3} \approx 2.1 \cdot 0.8660 \approx 1.82$ $\displaystyle y = r \sin \theta = 2.1 \cdot \sin \frac{7\pi }{3} \approx 2.1 \cdot 0.8660 \approx 1.82$

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Example Question #1 : Understanding Polar Coordinates

The polar coordinates of a point are $\left(2.1, \frac{7\pi }{3}\right )$ $\displaystyle \left(2.1, \frac{7\pi }{3}\right )$. Give its $\displaystyle x$-coordinate in the rectangular coordinate system (nearest hundredth).

Possible Answers:

-1.05 $\displaystyle -1.05$

1.82 $\displaystyle 1.82$

-1.82 $\displaystyle -1.82$

1.05 $\displaystyle 1.05$

4.20 $\displaystyle 4.20$

Correct answer:

1.05 $\displaystyle 1.05$

Explanation:

Given the polar coordinates $(r,\theta )$ $\displaystyle (r,\theta )$, the $\displaystyle x$-coordinate is $x= r \cos \theta$ $\displaystyle x= r \cos \theta$. We can find this coordinate by substituting $r = 2.1, \theta = \frac{7\pi }{3}$ $\displaystyle r = 2.1, \theta = \frac{7\pi }{3}$:

$x = r \cos \theta = 2.1 \cdot \cos \frac{7\pi }{3} = 2.1 \cdot 0.5 = 1.05$ $\displaystyle x = r \cos \theta = 2.1 \cdot \cos \frac{7\pi }{3} = 2.1 \cdot 0.5 = 1.05$

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Example Question #1 : Understanding Polar Coordinates

The polar coordinates of a point are $\left(1.2, \frac{2\pi }{5}\right )$ $\displaystyle \left(1.2, \frac{2\pi }{5}\right )$. Give its $\displaystyle y$-coordinate in the rectangular coordinate system (nearest hundredth).

Possible Answers:

1.26 $\displaystyle 1.26$

3.69 $\displaystyle 3.69$

1.14 $\displaystyle 1.14$

0.37 $\displaystyle 0.37$

3.88 $\displaystyle 3.88$

Correct answer:

1.14 $\displaystyle 1.14$

Explanation:

Given the polar coordinates $(r,\theta )$ $\displaystyle (r,\theta )$, the $\displaystyle y$-coordinate is $y= r \sin \theta$ $\displaystyle y= r \sin \theta$. We can find this coordinate by substituting $r = 1.2, \theta = \frac{2\pi }{5}$ $\displaystyle r = 1.2, \theta = \frac{2\pi }{5}$:

$y = r \cos \theta = 1.2 \cdot \sin \frac{2\pi }{5} \approx 1.2 \cdot 0.9511 \approx 1.14$ $\displaystyle y = r \cos \theta = 1.2 \cdot \sin \frac{2\pi }{5} \approx 1.2 \cdot 0.9511 \approx 1.14$

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Example Question #4 : Calculus Ii — Integrals

The polar coordinates of a point are $\left(1.2, \frac{2\pi }{5}\right )$ $\displaystyle \left(1.2, \frac{2\pi }{5}\right )$. Give its $\displaystyle x$-coordinate in the rectangular coordinate system (nearest hundredth).

Possible Answers:

3.69 $\displaystyle 3.69$

0.37 $\displaystyle 0.37$

3.88 $\displaystyle 3.88$

1.14 $\displaystyle 1.14$

1.26 $\displaystyle 1.26$

Correct answer:

0.37 $\displaystyle 0.37$

Explanation:

Given the polar coordinates $(r,\theta )$ $\displaystyle (r,\theta )$, the $\displaystyle x$-coordinate is $x= r \cos \theta$ $\displaystyle x= r \cos \theta$. We can find this coordinate by substituting $r = 1.2, \theta = \frac{2\pi }{5}$ $\displaystyle r = 1.2, \theta = \frac{2\pi }{5}$:

$x = r \cos \theta = 1.2 \cdot \cos \frac{2\pi }{5} \approx 1.2 \cdot 0.3090 \approx 0.37$ $\displaystyle x = r \cos \theta = 1.2 \cdot \cos \frac{2\pi }{5} \approx 1.2 \cdot 0.3090 \approx 0.37$

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High School Math : Understanding Polar Coordinates

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : Calculus Ii — Integrals

Example Question #1 : Understanding Polar Coordinates

Example Question #1 : Understanding Polar Coordinates

Example Question #4 : Calculus Ii — Integrals

All High School Math Resources

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