Trigonometry Examples

$(1, \frac{π}{4})$

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 $θ = \frac{π}{4}$ into the formulas.

$x = (1) \cos (\frac{π}{4})$

$y = (1) \sin (\frac{π}{4})$

Step 3

Multiply $\cos (\frac{π}{4})$ by $1$ .

$x = \cos (\frac{π}{4})$

$y = (1) \sin (\frac{π}{4})$

Step 4

The exact value of $\cos (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

$y = (1) \sin (\frac{π}{4})$

Step 5

Multiply $\sin (\frac{π}{4})$ by $1$ .

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

$y = \sin (\frac{π}{4})$

Step 6

The exact value of $\sin (\frac{π}{4})$ is $\frac{\sqrt{2}}{2}$ .

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

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

Step 7

The rectangular representation of the polar point $(1, \frac{π}{4})$ is $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ .

$(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$