Question

question given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. \tan 225^{\circ}

Explanation:

Step1: Determine the reference angle

The angle \(225^\circ\) is in the third quadrant. To find the reference angle, we subtract \(180^\circ\) from \(225^\circ\):
\(225^\circ - 180^\circ = 45^\circ\).

Step2: Recall the tangent function in the third quadrant

In the third quadrant, both sine and cosine are negative, so \(\tan\theta=\frac{\sin\theta}{\cos\theta}\) will be positive (negative divided by negative).

Step3: Evaluate \(\tan 45^\circ\)

We know that \(\tan 45^\circ = 1\). Since \(\tan 225^\circ\) has the same absolute value as \(\tan 45^\circ\) and is positive (third quadrant), we have:
\(\tan 225^\circ = \tan(180^\circ + 45^\circ) = \tan 45^\circ = 1\).

Answer:

1