Question

Arcsin(-0.5)+arcsin√3/2

Answer 1

Arcsin(-0.5)+arcsin√3/2 = - П/6 + П/3 = П/6

Answer 2

To calculate the expression, we'll first need to find the values of arcsin(-0.5) and arcsin(√3/2).

1. arcsin(-0.5): arcsin(-0.5) is the angle whose sine is -0.5. We know that the sine function is negative in the 3rd and 4th quadrants. So, the angle whose sine is -0.5 is -30 degrees or -π/6 radians.

2. arcsin(√3/2): arcsin(√3/2) is the angle whose sine is √3/2. We know that the sine function is positive in the 1st and 2nd quadrants. So, the angle whose sine is √3/2 is 60 degrees or π/3 radians.

Now, let's calculate the expression:

Arcsin(-0.5) + arcsin(√3/2) = -π/6 + π/3

To add these fractions, we need a common denominator. The common denominator for 6 and 3 is 6. So, we can rewrite the expression as:

= (-π/6 * 2/2) + (π/3 * 2/2) = (-2π/12) + (2π/6)

Now, we have a common denominator. Let's add the fractions:

= (2π/6) - (2π/12) = (2π - π)/12 = π/12

So, the final result of the expression Arcsin(-0.5) + arcsin(√3/2) is π/12 radians.