# trigonometry

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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 -

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

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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