sin a = 5/12 with angle ∠A lies in quadrant 2. find cos and tan

If the sin is 5/12 in the second quadrant, then x = -√[12^2 - 5^2] = -√119

So, the cosine = -√119 / 12 ....  and the tangent =  - 5/ √119 

First use sin^-1(5/12)  (or asin(5/12) which is the same thing).  This will give an angle in the first quadrant. 

Next subtract this angle from 180°, to give an angle whose sine is also 5/12.

Then use cos and tan on this angle (you should find that both cos and tan values are negative).

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