Question

If $\pi/2 < x < \pi$ and $\tan x = -3/4$, then $\cos x = ?$

• A. -3/5
• B. 3/5
• C. 4/5
• D. -4/5

Hint:

ASTC rule: All positive in Q1, Sin in Q2, Tan in Q3, Cos in Q4.

Answer 1

The Correct Option is D

Step 1: Concept
Trigonometric ratios in different quadrants.

Step 2: Analysis
The interval $\pi/2 < x < \pi$ is the second quadrant. In this quadrant, $\sin$ is positive, while $\cos$ and $\tan$ are negative.

Step 3: Calculation
$\tan x = -3/4$ (Opposite/Adjacent). Hypotenuse = $\sqrt{3^2 + 4^2} = 5$.
$\cos x = \text{Adjacent/Hypotenuse} = 4/5$. Since it's Q2, $\cos x = -4/5$.

Step 4: Conclusion
The value of $\cos x$ is -4/5. Final Answer: (D)