Find the Cartesian coordinates of a point on the unit circle where the angle is $135^{circ}$.

To find the Cartesian coordinates of a point on the unit circle where the angle is $135^{\circ}$, we use the unit circle equation:

$x = \cos(135^{\circ})$

$y = \sin(135^{\circ})$

First, we calculate the cosine and sine of $135^{\circ}$:

$\cos(135^{\circ}) = -\frac{\sqrt{2}}{2}$

$\sin(135^{\circ}) = \frac{\sqrt{2}}{2}$

So, the Cartesian coordinates are:

$(x, y) = \left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$

Given the angle $135^{circ}$ on the unit circle, we find the corresponding Cartesian coordinates as follows:

$x = cos(135^{circ})$

$y = sin(135^{circ})$

Using trigonometric identities, we get:

$cos(135^{circ}) = -cos(45^{circ}) = -frac{sqrt{2}}{2}$

$sin(135^{circ}) = sin(45^{circ}) = frac{sqrt{2}}{2}$

Thus, the Cartesian coordinates are:

$(x, y) = left(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

To find the Cartesian coordinates for $135^{circ}$ on the unit circle:

$x = cos(135^{circ}) = -frac{sqrt{2}}{2}$

$y = sin(135^{circ}) = frac{sqrt{2}}{2}$

Coordinates are:

$(x, y) = left(-frac{sqrt{2}}{2}, frac{sqrt{2}}{2}
ight)$

Start Using PopAi Today