Convert to Rectangular Coordinates (1,(5pi)/6)

$(1, \frac{5 π}{6})$

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 $r = 1$ and $θ = \frac{5 π}{6}$ into the formulas.

$(1) \cos (\frac{5 π}{6})$

$y = (1) \sin (\frac{5 π}{6})$

Multiply $\cos (\frac{5 π}{6})$ by $1$ .

$x = \cos (\frac{5 π}{6})$

$y = (1) \sin (\frac{5 π}{6})$

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.

$x = - \cos (\frac{π}{6})$

$y = (1) \sin (\frac{5 π}{6})$

The exact value of $\cos (\frac{π}{6})$ is $\frac{\sqrt{3}}{2}$ .

$x = - \frac{\sqrt{3}}{2}$

$y = (1) \sin (\frac{5 π}{6})$

Multiply $\sin (\frac{5 π}{6})$ by $1$ .

$x = - \frac{\sqrt{3}}{2}$

$y = \sin (\frac{5 π}{6})$

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

$x = - \frac{\sqrt{3}}{2}$

$y = \sin (\frac{π}{6})$

The exact value of $\sin (\frac{π}{6})$ is $\frac{1}{2}$ .

$x = - \frac{\sqrt{3}}{2}$

$y = \frac{1}{2}$

The rectangular representation of the polar point $(1, \frac{5 π}{6})$ is $(- \frac{\sqrt{3}}{2}, \frac{1}{2})$ .

$(- \frac{\sqrt{3}}{2}, \frac{1}{2})$

Convert to Rectangular Coordinates (1,(5pi)/6)

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