If #x = tan(1)#, #y = tan(2)# and #z = tan(3)#, then how do you place #x, y, z# in decreasing order?

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Answer 1 · 2015-06-17T18:06:18

x, z, y

#0 < 1 < pi/2# so #1# radian is in QI,

#sin(1) > 0# and #cos(1) > 0# so #tan(1) > 0#

#pi/2 < 2 < pi# so #2# radians is in Q2

#sin(2) > 0# and #cos(2) < 0# so #tan(2) < 0#

#2 < 3 < pi# so #3# radians is in Q2

#sin(3) > 0# and #cos(3) < 0# so #tan(3) < 0#

also #pi - 3# is quite small so #sin(3)# is much closer to #0# than #sin(2)# and #tan(3)# is also much closer to #0#.

So #tan(1) > tan(3) > tan(2)#

that is #x > z > y#