How do you solve and find the value of sin^-1(1/sqrt2)?

1 Answer
marfre
Mar 2, 2017

The angle = pi/2 = 45^@

Explanation:

sin^-1(1/sqrt(2)) says, give me the angle that has a sin of (1/sqrt(2)) = sqrt(2)/2

Either from a trig circle or from a 45^@-45^@-90^@ triangle, that angle would be either pi/4 = 45^@ or (3 pi)/4 = 135^@. However, the arcsin (sin^-1) function has a limited domain [-1, 1]and range [-pi/2, pi/2] = [-90^@, 90^@]. This means (3 pi)/4 = 135^@ is not a valid answer.

You can see this from the graph f(x) = arcsin(x) = sin^-1(x):
graph{arcsin(x) [-4.933, 4.932, -2.466, 2.467]}

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