To find the value of \( \tan 225^\circ \), we can follow these steps:
### Step 1: Identify the angle in the unit circle
The angle \( 225^\circ \) is located in the third quadrant of the unit circle.
### Step 2: Find the reference angle
The reference angle for \( 225^\circ \) can be found by subtracting \( 180^\circ \):
\[
225^\circ - 180^\circ = 45^\circ
\]
So, the reference angle is \( 45^\circ \).
### Step 3: Determine the sign of the tangent function
In the third quadrant, the tangent function is positive.
### Step 4: Use the value of the tangent for the reference angle
We know that:
\[
\tan 45^\circ = 1
\]
### Step 5: Apply the sign to the reference angle's tangent value
Since \( \tan \) is positive in the third quadrant:
\[
\tan 225^\circ = \tan 45^\circ = 1
\]
### Final Answer
Thus, the value of \( \tan 225^\circ \) is:
\[
\boxed{1}
\]
---
To find the value of \( \tan 225^\circ \), we can follow these steps:
### Step 1: Identify the angle in the unit circle
The angle \( 225^\circ \) is located in the third quadrant of the unit circle.
### Step 2: Find the reference angle
The reference angle for \( 225^\circ \) can be found by subtracting \( 180^\circ \):
\[
...
