Trigonometry Examples

$(- 1, 270)$

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 $r = - 1$ and $θ = 270$ into the formulas.

$x = (- 1) \cos (270)$

$y = (- 1) \sin (270)$

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 third quadrant.

$x = - 1 (- \cos (90))$

$y = (- 1) \sin (270)$

Step 4

The exact value of $\cos (90)$ is $0$ .

$x = - 1 (- 0)$

$y = (- 1) \sin (270)$

Step 5

Multiply $- 1 (- 0)$ .

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Step 5.1

Multiply $- 1$ by $0$ .

$x = - 1 \cdot 0$

$y = (- 1) \sin (270)$

Step 5.2

Multiply $- 1$ by $0$ .

$x = 0$

$y = (- 1) \sin (270)$

$x = 0$

$y = (- 1) \sin (270)$

Step 6

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

$x = 0$

$y = - 1 (- \sin (90))$

Step 7

The exact value of $\sin (90)$ is $1$ .

$x = 0$

$y = - 1 (- 1 \cdot 1)$

Step 8

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

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Step 8.1

Multiply $- 1$ by $1$ .

$x = 0$

$y = - 1 \cdot - 1$

Step 8.2

Multiply $- 1$ by $- 1$ .

$x = 0$

$y = 1$

$x = 0$

$y = 1$

Step 9

The rectangular representation of the polar point $(- 1, 270)$ is $(0, 1)$ .

$(0, 1)$