Trigonometry Examples

$(0, - \frac{7 π}{6})$

Step 1

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

$x = r c o s θ$

$y = r s i n θ$

Step 2

Substitute in the known values of $r = 0$ and $θ = - \frac{7 π}{6}$ into the formulas.

$x = (0) \cos (- \frac{7 π}{6})$

$y = (0) \sin (- \frac{7 π}{6})$

Step 3

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$x = 0 \cos (\frac{5 π}{6})$

$y = (0) \sin (- \frac{7 π}{6})$

Step 4

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.

$x = 0 (- \cos (\frac{π}{6}))$

$y = (0) \sin (- \frac{7 π}{6})$

Step 5

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

$x = 0 (- \frac{\sqrt{3}}{2})$

$y = (0) \sin (- \frac{7 π}{6})$

Step 6

Multiply $0 (- \frac{\sqrt{3}}{2})$ .

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Step 6.1

Multiply $- 1$ by $0$ .

$x = 0 (\frac{\sqrt{3}}{2})$

$y = (0) \sin (- \frac{7 π}{6})$

Step 6.2

Multiply $0$ by $\frac{\sqrt{3}}{2}$ .

$x = 0$

$y = (0) \sin (- \frac{7 π}{6})$

$x = 0$

$y = (0) \sin (- \frac{7 π}{6})$

Step 7

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$x = 0$

$y = 0 \sin (\frac{5 π}{6})$

Step 8

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

$x = 0$

$y = 0 \sin (\frac{π}{6})$

Step 9

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

$x = 0$

$y = 0 (\frac{1}{2})$

Step 10

Multiply $0$ by $\frac{1}{2}$ .

$x = 0$

$y = 0$

Step 11

The rectangular representation of the polar point $(0, - \frac{7 π}{6})$ is $(0, 0)$ .

$(0, 0)$