Question
Use the Unit Circle to find the value. tan 135° = (1 point) Responses 1 1 −1 negative 1 3–√ square root of 3 −3–√
Answers
Answered by
GPT-4o mini
To find the value of \(\tan 135^\circ\) using the unit circle, we can follow these steps:
1. **Identify the Angle**: \(135^\circ\) is in the second quadrant.
2. **Reference Angle**: The reference angle for \(135^\circ\) is \(180^\circ - 135^\circ = 45^\circ\).
3. **Value of Tangent**: The tangent function is given by the ratio of the sine and cosine. In the second quadrant, the cosine is negative and the sine is positive. For the angle \(45^\circ\), we have:
\[
\tan 45^\circ = 1
\]
4. **Determine the Sign**: Since \(135^\circ\) is in the second quadrant, the tangent (which is sine over cosine) will be negative:
\[
\tan 135^\circ = -\tan 45^\circ = -1
\]
Thus, the value of \(\tan 135^\circ\) is \(-1\).
The correct response is:
**−1**.
1. **Identify the Angle**: \(135^\circ\) is in the second quadrant.
2. **Reference Angle**: The reference angle for \(135^\circ\) is \(180^\circ - 135^\circ = 45^\circ\).
3. **Value of Tangent**: The tangent function is given by the ratio of the sine and cosine. In the second quadrant, the cosine is negative and the sine is positive. For the angle \(45^\circ\), we have:
\[
\tan 45^\circ = 1
\]
4. **Determine the Sign**: Since \(135^\circ\) is in the second quadrant, the tangent (which is sine over cosine) will be negative:
\[
\tan 135^\circ = -\tan 45^\circ = -1
\]
Thus, the value of \(\tan 135^\circ\) is \(-1\).
The correct response is:
**−1**.