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Step-by-step explanation:

sin∅=-3/4 in 4 quadrant which sine is negative there

using soh cah toa

sin=opp/hyp

where our opp=-3 and our hyp=4

using pythagoras theorem

hyp²=opp²+adj²

(4)²=(-3)²+adj²

16=9+adj²

16-9=adj²

adj²=7

adj=√7

from soh cah toa

cos∅=adj/hyp

cos∅=√7/4

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