Question

Arcsin(-1)-3/2*arccos1/2

Answer 1

(arcsin(-1)-3)/(2.arccos1/2)= (-π/2-3)/2.π/3

Answer 2

To simplify the expression \arcsin(-1) - \frac{3}{2} \arccos\left(\frac{1}{2}), let's break it down step by step:

1. $\arcsin(-1)$: The arcsin function returns values in the range $-\pi/2$ to $\pi/2$, and $\arcsin(-1)$ corresponds to $-\pi/2$ because it's the angle whose sine is -1.

2. $\arccos(1/2)$: The arccos function returns values in the range $0$ to $\pi$, and $\arccos(1/2)$ corresponds to $\pi/3$ because it's the angle whose cosine is $1/2$.

Now, we can plug these values into the expression:

\arcsin(-1) - \frac{3}{2} \arccos\left(\frac{1}{2} = $-\frac{\pi}{2} - \frac{3}{2} \cdot \frac{\pi}{3}$

Now, simplify the expression:

$-\frac{\pi}{2} - \frac{3}{2} \cdot \frac{\pi}{3} = -\frac{\pi}{2} - \frac{\pi}{2} = -\pi$

So, \arcsin(-1) - \frac{3}{2} \arccos\left(\frac{1}{2} simplifies to $-\pi$.