Trigonometry Examples

$(6, 180)$

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 $r = 6$ and $θ = 180$ into the formulas.

$x = (6) \cos (180)$

$y = (6) \sin (180)$

Step 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.

$x = 6 (- \cos (0))$

$y = (6) \sin (180)$

Step 4

The exact value of $\cos (0)$ is $1$ .

$x = 6 (- 1 \cdot 1)$

$y = (6) \sin (180)$

Step 5

Multiply $6 (- 1 \cdot 1)$ .

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Step 5.1

Multiply $- 1$ by $1$ .

$x = 6 \cdot - 1$

$y = (6) \sin (180)$

Step 5.2

Multiply $6$ by $- 1$ .

$x = - 6$

$y = (6) \sin (180)$

$x = - 6$

$y = (6) \sin (180)$

Step 6

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

$x = - 6$

$y = 6 \sin (0)$

Step 7

The exact value of $\sin (0)$ is $0$ .

$x = - 6$

$y = 6 \cdot 0$

Step 8

Multiply $6$ by $0$ .

$x = - 6$

$y = 0$

Step 9

The rectangular representation of the polar point $(6, 180)$ is $(- 6, 0)$ .

$(- 6, 0)$