QuestionIf $\tan \theta=-\frac{1}{3}$ , in which quadrants can $\theta$ be located? Check all that apply: 1, 2, 3, or 4.

Studdy Solution

STEP 1

Assumptions1. The tangent of the angle $\theta$ is given as $-\frac{1}{3}$ . . $\theta$ is an angle in standard position, which means its initial side is on the positive x-axis.
3. We need to find in which quadrant(s) the terminal side of $\theta$ could be.

STEP 2

We know that the tangent of an angle is the ratio of the y-coordinate to the x-coordinate of a point on the unit circle. The sign of the tangent depends on the signs of the y and x coordinates.

STEP 3

The tangent is negative when the y and x coordinates have different signs. This happens in Quadrant II (where x is negative and y is positive) and Quadrant IV (where x is positive and y is negative).

STEP 4

Therefore, given that $\tan \theta=-\frac{1}{3}$ , the terminal side of $\theta$ could be in Quadrant II or Quadrant IV.
The solution is Quadrant II and Quadrant IV.

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