QuestionIf $\sin \theta=\frac{2}{5}$ , which quadrants could the angle $\theta$ be in? Check all that apply: Quadrant 1, 2, 3, 4.

Studdy Solution

STEP 1

Assumptions1. The sine of an angle $\theta$ is given as $\frac{}{5}$ . $\theta$ is an angle in standard position3. We are asked to find the possible quadrants for the terminal side of $\theta$

STEP 2

The sine of an angle is positive in the first and second quadrants. This is due to the definition of sine as the y-coordinate of the point on the unit circle determined by the angle. In the first and second quadrants, the y-coordinate is positive.

STEP 3

Since the given $\sin \theta=\frac{2}{5}$ is positive, the terminal side of $\theta$ could be in Quadrant1 or Quadrant2.

STEP 4

Therefore, the terminal side of $\theta$ could be in Quadrant1 and Quadrant2.

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