Trigonometry
Principal Value
MMTS_Full_Test_04
Grade 12
Question:
$x=\cos^{-1}(\cos 4)$, $y=\sin^{-1}(\sin 3)$, $z=\tan^{-1}(\tan 2)$, then $xyz=$
$(2\pi-4)(\pi-3)(2-\pi)$
$\pi^3$
$(4-2\pi)(3-\pi)(2-\pi)$
$(4-\pi)(3-\pi)(2-\pi)$
Step-by-Step Solution
Key Concept: $\cos^{-1}(\cos 4)=2\pi-4$; $\sin^{-1}(\sin 3)=\pi-3$; $\tan^{-1}(\tan 2)=2-\pi$
$x=2\pi-4$, $y=\pi-3$, $z=2-\pi$. $xyz=(2\pi-4)(\pi-3)(2-\pi)$.
Correct Answer: 1