1)sin?=-1/2, 180<?<270, find tan? 2)cot?=-1,90<?<180, find cos? 3)csc?=v2,p/2<?<
ID: 3099070 • Letter: 1
Question
1)sin?=-1/2, 180<?<270, find tan? 2)cot?=-1,90<?<180, find cos? 3)csc?=v2,p/2<?<p, find cot? 4)sec?=2v3/3,3p/2<?<2p, find sin? 5)sin?=-1/2 and cos?>0, find tan? 6)tan?=1 and sin?<0 find cos? 7) cos?=1/2 and tan?=v3, find csc? 8) tan?=1 and sin?=v2/2, find sec? 9)cos?=-1/2 and sin?=v3/2 find cot? 10) sec?=2v3/3 and sin?=-1/2 find cot? 1)sin?=-1/2, 180<?<270, find tan? 2)cot?=-1,90<?<180, find cos? 3)csc?=v2,p/2<?<p, find cot? 4)sec?=2v3/3,3p/2<?<2p, find sin? 5)sin?=-1/2 and cos?>0, find tan? 6)tan?=1 and sin?<0 find cos? 7) cos?=1/2 and tan?=v3, find csc? 8) tan?=1 and sin?=v2/2, find sec? 9)cos?=-1/2 and sin?=v3/2 find cot? 10) sec?=2v3/3 and sin?=-1/2 find cot?Explanation / Answer
Looking at a unit circle and knowing that tan = sin/cos, sin = 1/csc, and cos = 1/sec, we can get: 1)sin x = -1 so x = 210 or 330
180 < x < 270 so x = 210
tan 210 = v(3) / 3 2) cot x = -1 ? tan x = -1 so x = 135 or 315 90 < x < 180 so x = 135 cos 135 = -v2 / 2 3) csc x = v2 ? sin x = 1/v2 = v2 / 2 so x = 135 or 315 p/2 < x < p so x = 135 cot x = -1 4) sec x = 2v3 / 3 ? cos x = 3 / 2v3 = v3 / 2 so x = 30 or 330 3p/2 < x < 2p so x = 330 sin 330 = -1 / 2 5) sin x = -1 / 2 so x = 210 or 330 cos x > 0 so x = 330 tan 330 = -v3 / 3 6) tan x = 1 so x = 45 or 225 sin x < 0 so x = 225 cos 225 = -v2 / 2 7) cos x = 1/2 so x = 60 or 300 tan x = v3 so x = 60 csc x = 1/sinx = 1/ (1/2) = 2 8) tan x = 1 so x = 45 or 225 sin x = v2 / 2 so x = 45 sec x = 1/cosx = 1 / (v2 / 2) = v2 9) cos x = -1 / 2 so x = 120 or 240 sin x = v3 / 2 so x = 120 cot x = cosx / sinx = (-1 /2) / (v3 / 2) = -v3 / 3 10) sec x = 2v3 / 3 ? cos x = v3 / 2 so x = 30 or 330 sin x = -1/2 so x = 330 cot x = cos x / sin x = (v3 / 2)/(-1/2) = -v3 Please let me know if there's anything I can clarify or help with :)
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