Question

Which value is a solution for the equation tan(x/2)=1?

A. π/2

B. 3π/2

C. 3π/4

D. π/4

Answer 1

tanx=1, x=phi/4+kpi

Answer 2

use this fact to solve tan(x/2)=1

Answer 3

Wait, do you mean x=pi/4+kpi or do you actually mean the "phi"?

Answer 4

no what i mean is the values that can make tangent 1 are pi/4+kpi
this a general solution. you need to derive you solution from this

Answer 5

your x here is x/2! do you get it

Answer 6

Yes, I get it :o Give me a moment to work it out

Answer 7

Okay!

Answer 8

Hm, I'm actually getting sort of confused. :< Would I plug in "pi/4+kpi" into the "x" in tan(x/2)=1?

Answer 9

No, tan(x/2)=1 means that x/2=pi/4+kpi solve for x

Answer 10

Ahhh, what would be done with "k", then?

Answer 11

i'm just showing you that if tan(x)=1 that means x must be x=pi/4+kpi
x being an angle! so the same reasoning
there some angles such that tan(x/2)=1
we know that those angles much be pi/4+kpi (k is the period)
so x/2=pi/4+kpi

Answer 12

just leave it

Answer 13

actually you question should state something about the from ?<x<?
since they give you the choices
what we are doing is the general solution!!

Answer 14

@nincompoop what do think lol

Answer 15

Hm, I'm still getting rather lost x) Would it be closer to pi/4 as a solution, then?

Answer 16

oh I was not reading, I accidentally clicked it and I just didn't bother

Answer 17

haha well x/2=pi/4+kpi how do you solve for x here?
do you know how

Answer 18

@nincompoop oh, alright! xD

Answer 19

did your question give interval for x? like 0<x<pi/2 or something

Answer 20

you will have to think tangent in terms of sin/cosine

Answer 21

oh wait you have options

Answer 22

well even with that, those options are not accurate if there is not interval?

Answer 23

that equation will simply be solved in general terms?

Answer 24

tangent is positive in two quadrants

Answer 25

yeah you can use tan = sin/cos concept

Answer 26

sin = y
cos = x

x=y = 1
your slope is at a 45 degree angle which is 180/4 or pi/4

Answer 27

well that's pi/4+kpi no?

Answer 28

depends on the period

Answer 29

yeah, but that is your basis

Answer 30

he hasn't given any other info to use to solve for a specific interval
that's why im saying the solution is in general temrs?

Answer 31

wondered why there are options like that xD

Answer 32

x = pi/2 = 90
90/2 = 45

Answer 33

tan 45 = 1

Answer 34

well tan225=1 too? haha

Answer 35

that's 5pi/4

Answer 36

yes, but can you get tan 225 with any of the options? I doubt

Answer 37

anyway for this question the solution is pi/2.
but the question is not accurate as i said perhaps there is a reason

Answer 38

it is accurate, but slightly tricky

Answer 39

But let's talk in general! this equation as it is has more than one solution
without considering options

Answer 40

time to sleep haha not for trig xD