How do you find the exact value of #sin u = -sqrt(5) / 6# in quadrant IV?

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Answer 1 · 2016-02-16T07:29:12

#u=338.119^@#

from the given

#sin u=(-sqrt5)/6#

#u=sin^-1 ((-sqrt5)/6)#

#u=-21.8809^@#

At the 4th quadrant

#u=338.119^@#

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Answer 2 · 2016-02-16T07:35:09

#u=338.12^o#

Function sine is negative in 3rd and 4th quadrants.

Now for #sin u=-sqrt5/6#, we first find #sin^(-1)-(sqrt5/6)# using a scientific calculator.

As #-(sqrt5/6)=-0.3727#, #u=sin^(-1)-(sqrt5/6)=-21.88^o# or #360-21.88^o=338.12^o#, which is in fourth quadrant.

Other solution could be #(180+21.88)^o# or #201.88^o# in third quadrant, which is not permissible.