The algebraic sign of tan θ is positive in the first and third quadrants.
To understand this, we need to recall the signs of the trigonometric functions in the four quadrants:
- First Quadrant (0° to 90°): All trigonometric functions are positive. Hence, tan θ is positive.
- Second Quadrant (90° to 180°): Sine is positive, but cosine is negative, making tan θ negative (since tan θ = sin θ/cos θ).
- Third Quadrant (180° to 270°): Both sine and cosine are negative, resulting in a positive tan θ (as the division of two negative numbers is positive).
- Fourth Quadrant (270° to 360°): Cosine is positive, but sine is negative, leading to a negative tan θ.
In summary, tan θ is positive in the first and third quadrants, where the sine and cosine either both share the same sign (third quadrant) or are both positive (first quadrant).