cutiecomittee123
  • cutiecomittee123
If sin x = 3/5 and x is in quadrant 2, what is the value of tan x/2?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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RCCB
  • RCCB
http://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.771795.html this might help
cutiecomittee123
  • cutiecomittee123
Well I think it is supposed to be solved using trig identities
TrojanPoem
  • TrojanPoem
cosx = 1- 2 sin^2 (x/2) cosx - 1 = -2sin^2(x/2) -0.5cosx +0.5 = sin^2(x/2) cosx = -4/5 (2nd quarter) sinx/2 = sqrt(-0.5 * -4/5 + 0.5) = 3sqrt(10)/10 |dw:1446760327411:dw| tanx/2 = -3sqrt(10)/sqrt(10) = -3 (2nd quarter) Any mistakes ?

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cutiecomittee123
  • cutiecomittee123
I get tan x = -3/4 since cos= -4/5 and sin=3/5 so (3/5)/(-4/5)=-3/4
cutiecomittee123
  • cutiecomittee123
but then since its tan x/2 I think you divide that by two so tan x/2=(-3/4)/2 tanx/2=-3/8
TrojanPoem
  • TrojanPoem
NO
TrojanPoem
  • TrojanPoem
sin(60) = sqrt(3)/2 so sin(30) = sqrt(3)/ 4 ??? of course not , you have to use half angle identity
TrojanPoem
  • TrojanPoem
cosx = 1- 2 sin^2 (x/2) cosx = 2cos^2(x/2) - 1 cosx = cos^2x/2 - sin^2x/2 sinx = 2 sinx/2 cosx/2
TrojanPoem
  • TrojanPoem
tanx = 2tanx/2 / 1- tan^2x/2
TrojanPoem
  • TrojanPoem
That's the double angle identities , you can derive the half angle ones from them.
cutiecomittee123
  • cutiecomittee123
Okay yeah I have those in my notes. But I dont understand where and how they are used when trying to solve these kind of questions.
cutiecomittee123
  • cutiecomittee123
??? liek I see that you plugged them in but how did you know that and when do you use this type of identity versus other ones?
TrojanPoem
  • TrojanPoem
It's easy to notice when to use them, if it's asking for ex for sin2x and the given is sinx so you have to use this identities , sin4x and you 're given sin2x or sinx or sin0.5x it asks for sin0.5x and you have sin4x and so on.
TrojanPoem
  • TrojanPoem
always think of them when the angles are double or half in either sin or cos or tan or cot or cosec or sec xD
cutiecomittee123
  • cutiecomittee123
okay well it looks like tan x = 3 not -3
cutiecomittee123
  • cutiecomittee123
I am still very confused with this math. I am going to try another question and see if it will help my understanding
RCCB
  • RCCB
im pretty sure its x=3
TrojanPoem
  • TrojanPoem
@RCCB , x is in quadrant 2, is in the second quarter so it's negative.
TrojanPoem
  • TrojanPoem
180 >= x >= 90 (divide the whole equation over 2) 90 >= x/2 >= 45 (first quarter ) so x/2 in the 1st , x in the 2nd
RCCB
  • RCCB
oh

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