Find the sine, cosine, and tangent values of the angle $225^{circ}$ using the unit circle

To find the sine, cosine, and tangent values of the angle $225^{\circ}$ using the unit circle, follow these steps:

1. Convert the angle to radians: $225^{\circ} = 225 \times \frac{\pi}{180} = \frac{5\pi}{4}$

2. Determine the reference angle: The reference angle for $225^{\circ}$ is $225^{\circ} – 180^{\circ} = 45^{\circ}$

3. Use the unit circle to find the coordinates of the reference angle in the third quadrant, where both sine and cosine are negative. The coordinates for $45^{\circ}$ are $\left(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$, so for $225^{\circ}$, they will be $\left(-\frac{\sqrt{2}}{2}, -\frac{\sqrt{2}}{2}\right)$.

4. From these coordinates, we get:

$\sin(225^{\circ}) = -\frac{\sqrt{2}}{2}$

$\cos(225^{\circ}) = -\frac{\sqrt{2}}{2}$

$\tan(225^{\circ}) = \frac{\sin(225^{\circ})}{\cos(225^{\circ})} = \frac{-\frac{\sqrt{2}}{2}}{-\frac{\sqrt{2}}{2}} = 1$

To solve for the sine, cosine, and tangent of $225^{circ}$ using the unit circle:

1. Convert the angle: $225^{circ} = frac{5pi}{4}$ radians.

2. Reference angle: $45^{circ}$ in the third quadrant.

3. Coordinates: $left(-frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$.

Results:

$sin(225^{circ}) = -frac{sqrt{2}}{2}$

$cos(225^{circ}) = -frac{sqrt{2}}{2}$

$ an(225^{circ}) = 1$

Using the unit circle,

$225^{circ} = frac{5pi}{4}$ radians.

Reference angle: $45^{circ}$.

Coordinates: $left(-frac{sqrt{2}}{2}, -frac{sqrt{2}}{2}
ight)$.

Results:

$sin(225^{circ}) = -frac{sqrt{2}}{2}$

$cos(225^{circ}) = -frac{sqrt{2}}{2}$

$ an(225^{circ}) = 1$

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