Question

in which quadrant is sine negative, cosine positive, and tangent negative? (1 point)
○ quadrant iv
○ quadrant i
○ quadrant iii
○ quadrant ii

Explanation:

1. Recall the sign rules of trigonometric functions in each quadrant:

• In Quadrant I: Sine ($\sin$), Cosine ($\cos$), and Tangent ($\tan$) are all positive (since $\sin=\frac{y}{r}$, $\cos=\frac{x}{r}$, $\tan=\frac{y}{x}$, and $x,y,r>0$ here).
• In Quadrant II: Sine is positive ( $y>0$), Cosine is negative ($x < 0$), Tangent is negative ($\frac{y}{x}<0$ as $y>0,x < 0$).
• In Quadrant III: Sine is negative ($y < 0$), Cosine is negative ($x < 0$), Tangent is positive ($\frac{y}{x}>0$ as $y < 0,x < 0$).
• In Quadrant IV: Sine is negative ($y < 0$), Cosine is positive ($x>0$), Tangent is negative ($\frac{y}{x}<0$ as $y < 0,x>0$).

1. We need the quadrant where $\sin$ is negative, $\cos$ is positive, and $\tan$ is negative. From the above rules, Quadrant IV satisfies these conditions.

Answer:

A. Quadrant IV