Find the exact value of tan x (without finding x )if sin x - cos x =0.2 and sin

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sin x > 0 => x is in the first or second quadrant Think of a right triangle with sides opp, adj, and hyp: sin x = opp / hyp cos x = adj / hyp So sin x - cos x = (opp / hyp) - (adj / hyp) = (opp - adj) / hyp =.2 = 1 / 5 => opp - adj = 1, hyp = 5 5^2 = opp^2 + adj^2, try opp = 4, adj = 3 ... 4^2 + 3^2 = 16 + 9 =25 = 5^2 tan x = opp / adj = 4/3 Check: arcsin(4/5) = 0.92729521, sin(0.92729521) - cos(0.92729521)= .2, tan(0.92729521) = 4/3

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