Convert to Rectangular Coordinates (7,(2pi)/3) - MathMaster

Math

$(7, \frac{2 π}{3})$

Use the conversion formulas to convert from polar coordinates to rectangular coordinates.

$x = r c o s θ$

$y = r s i n θ$

Substitute in the known values of $r = 7$ and $θ = \frac{2 π}{3}$ into the formulas.

$(7) \cos (\frac{2 π}{3})$

$y = (7) \sin (\frac{2 π}{3})$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.

$x = 7 (- \cos (\frac{π}{3}))$

$y = (7) \sin (\frac{2 π}{3})$

The exact value of $\cos (\frac{π}{3})$ is $\frac{1}{2}$ .

$x = 7 (- \frac{1}{2})$

$y = (7) \sin (\frac{2 π}{3})$

Multiply $7 (- \frac{1}{2})$ .

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Multiply $- 1$ by $7$ .

$x = - 7 (\frac{1}{2})$

$y = (7) \sin (\frac{2 π}{3})$

Combine $- 7$ and $\frac{1}{2}$ .

$x = \frac{- 7}{2}$

$y = (7) \sin (\frac{2 π}{3})$

$x = \frac{- 7}{2}$

$y = (7) \sin (\frac{2 π}{3})$

Move the negative in front of the fraction.

$x = - \frac{7}{2}$

$y = (7) \sin (\frac{2 π}{3})$

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$x = - \frac{7}{2}$

$y = 7 \sin (\frac{π}{3})$

The exact value of $\sin (\frac{π}{3})$ is $\frac{\sqrt{3}}{2}$ .

$x = - \frac{7}{2}$

$y = 7 (\frac{\sqrt{3}}{2})$

Combine $7$ and $\frac{\sqrt{3}}{2}$ .

$x = - \frac{7}{2}$

$y = \frac{7 \sqrt{3}}{2}$

The rectangular representation of the polar point $(7, \frac{2 π}{3})$ is $(- \frac{7}{2}, \frac{7 \sqrt{3}}{2})$ .

$(- \frac{7}{2}, \frac{7 \sqrt{3}}{2})$

Convert to Rectangular Coordinates (7,(2pi)/3)

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