Question

Arccos ( - 1/2) + arcsin √3/2

Answer 1

Ответ:

$\pi$

Объяснение:

$\arccos \bigg (-\dfrac{1}{2} \bigg )+\arcsin \dfrac{\sqrt{3}}{2}=\pi-\arccos \dfrac{1}{2}+\dfrac{\pi}{3}=\pi-\dfrac{\pi}{3}+\dfrac{\pi}{3}=\pi;$

Answer 2

To find the value of arccos(-1/2) + arcsin(√3/2), you can use the trigonometric identities and values of these trigonometric functions at specific angles.

1. First, calculate arccos(-1/2):

The cosine function is negative in the second and third quadrants of the unit circle. In the second quadrant, the reference angle corresponding to cos(-1/2) is π/3 radians (or 60 degrees). So, arccos(-1/2) = π - π/3 = (3π/3) - (π/3) = (2π/3) radians.

2. Next, calculate arcsin(√3/2):

The sine function is positive in the first and second quadrants of the unit circle. In the first quadrant, the reference angle corresponding to sin(√3/2) is π/6 radians (or 30 degrees). So, arcsin(√3/2) = π/6 radians.

Now, you can add these two values:

arccos(-1/2) + arcsin(√3/2) = (2π/3) + (π/6) = (4π/6) + (π/6) = (5π/6) radians.

So, arccos(-1/2) + arcsin(√3/2) = (5π/6) radians.