Question

Arccos 1/2 +arcsin√2/2

Answer 1

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Answer 2

To find the value of the expression "arccos(1/2) + arcsin(√2/2)," we'll first determine the individual values of each trigonometric function and then add them together.

1. arccos(1/2): The arccosine function (arccos) gives the angle whose cosine is the given value. The cosine of π/3 radians (60 degrees) is 1/2.

arccos(1/2) = π/3

2. arcsin(√2/2): The arcsine function (arcsin) gives the angle whose sine is the given value. The sine of π/4 radians (45 degrees) is √2/2.

arcsin(√2/2) = π/4

Now, we add the two angles:

π/3 + π/4

To add these fractions, we need a common denominator, which is 12:

π/3 = (4π)/12 π/4 = (3π)/12

Now, adding them:

(4π)/12 + (3π)/12 = (7π)/12

So, the value of the expression is (7π)/12.