Posted by **kiko** on Sunday, April 15, 2012 at 12:06pm.

given that sin alpha/2 = 2/3, and that alpha/2 is in quadrant II, determine the exact values of all trig functions for alpha.

- trigonometry -
**Reiny**, Sunday, April 15, 2012 at 12:37pm
let alpha/2 = A/2

sin A/2 = 2/3

then cos A/2 = √5/3

sin A = 2(sin A/2)(cos A/2) = 2(2/3)(√5/3) = 4√5/9

make a sketch,

opposite = 4√5, hypotenuse = 9

adj^2 + 80 = 81

adj = 1

sin alpha = 4√5/9

cos alpha= 1/9

tan alpha = 4√5

I am sure you can find the three reciprocal values

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