QuestionIf $\cos \theta=\frac{1}{9}$ , in which quadrants could the angle $\theta$ be located? (Check all that apply)

Studdy Solution

STEP 1

Assumptions1. We are given that $\cos \theta=\frac{1}{9}$ . . $\theta$ is an angle in standard position.
3. We need to find the possible quadrants for the terminal side of $\theta$ .

STEP 2

We know that the cosine function, $\cos \theta$ , is positive in both Quadrant1 and Quadrant4 in standard position. This is often remembered by the acronym "All Students Take Calculus" (ASTC), where each letter represents a quadrant (1 to4) and the trigonometric functions that are positive in that quadrant. 'A' stands for all (Quadrant1 where all trigonometric functions are positive), '' stands for sine (Quadrant2 where only sine is positive), '' stands for tangent (Quadrant where only tangent is positive), and 'C' stands for cosine (Quadrant4 where only cosine is positive).

STEP 3

Since $\cos \theta=\frac{1}{9}$ is positive, the terminal side of $\theta$ could be in Quadrant1 or Quadrant.
So, the terminal side of $\theta$ could be in Quadrant1 and Quadrant.

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