Trigonometry Examples

$(\frac{π}{2}, 2)$

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 $r = \frac{π}{2}$ and $θ = 2$ into the formulas.

$x = (\frac{π}{2}) \cos (2)$

$y = (\frac{π}{2}) \sin (2)$

Step 3

Evaluate $\cos (2)$ .

$x = \frac{π}{2} \cdot - 0.41614683$

$y = (\frac{π}{2}) \sin (2)$

Step 4

Multiply $\frac{π}{2} \cdot - 0.41614683$ .

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Step 4.1

Combine $\frac{π}{2}$ and $- 0.41614683$ .

$x = \frac{π \cdot - 0.41614683}{2}$

$y = (\frac{π}{2}) \sin (2)$

Step 4.2

Multiply $π$ by $- 0.41614683$ .

$x = \frac{- 1.30736384}{2}$

$y = (\frac{π}{2}) \sin (2)$

$x = \frac{- 1.30736384}{2}$

$y = (\frac{π}{2}) \sin (2)$

Step 5

Divide $- 1.30736384$ by $2$ .

$x = - 0.65368192$

$y = (\frac{π}{2}) \sin (2)$

Step 6

Evaluate $\sin (2)$ .

$x = - 0.65368192$

$y = \frac{π}{2} \cdot 0.90929742$

Step 7

Multiply $\frac{π}{2} \cdot 0.90929742$ .

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Step 7.1

Combine $\frac{π}{2}$ and $0.90929742$ .

$x = - 0.65368192$

$y = \frac{π \cdot 0.90929742}{2}$

Step 7.2

Multiply $π$ by $0.90929742$ .

$x = - 0.65368192$

$y = \frac{2.85664211}{2}$

$x = - 0.65368192$

$y = \frac{2.85664211}{2}$

Step 8

Divide $2.85664211$ by $2$ .

$x = - 0.65368192$

$y = 1.42832105$

Step 9

The rectangular representation of the polar point $(\frac{π}{2}, 2)$ is $(- 0.65368192, 1.42832105)$ .

$(- 0.65368192, 1.42832105)$