Trigonometry & Inverse Trigonometry
Quadrant — Evaluating Expression in Terms of sin x
nta_pyq_2024_apr
Grade 11
Question:
If $\sin x=-\dfrac{3}{5}$, where $\pi<x<\dfrac{3\pi}{2}$, then $80\left(\tan^2 x-\cos x\right)$ is equal to
Step-by-Step Solution
Key Concept: $\pi<x<3\pi/2$ (third quadrant): $\sin x=-3/5\Rightarrow\cos x=-4/5$, $\tan x=3/4$.
$\tan x=3/4$, $\cos x=-4/5$. $80(9/16+4/5)=45+64=109$.
Correct Answer: 2