Question

Solve: (tan x - 1)(tan x - √3) = 0 0≤Ɵ<2π

Answer 1

tanx-1=0
tanx-sqrt(3)=0
tanx=1
tanx=sqrt(3)
for tanx=1, x=pi/4
tangent is also positive in the 3rd quadrant, so subtract pi/4 from 3pi/2 to get your second answer for this half of the equation.
follow the same rules for tanx=sqrt(3)

Answer 2

Where is the 3pi/2 come from ?

Answer 3

3pi/2-pi/4 will give you a solution in the 3rd quadrant

Answer 4

where tangent is also positive

Answer 5

its the same as pi/4+pi

Answer 6

pi/4+pi=3pi/2-pi/4=5pi/4

Answer 7

Sorry if it's a silly questions but how is pi/4 + pi = 3pi/2 ?
can you please explain this part, cuz I'm really confuse in class too about all this pi thing

Answer 8

\[\frac{\pi}{4}+\pi=\frac{\pi}{4}+\frac{4\pi}{4}=\frac{\pi+4\pi}{4}=\frac{5\pi}{4}\]

Answer 9

pi/4+pi does not equal 3pi/2
it equals 3pi/2-pi/4

Answer 10

both pi/4+pi and 3pi/2-pi/4 equal 5pi/4

Answer 11

see how i multiplied pi above by 4/4, this is to get each term with an LCD

Answer 12

then the addition is simple

Answer 13

i've only given you 2 solutions so far.
pi/4 and 5pi/4. there are 2 more solutions resulting from:
tanx=sqrt(3)

Answer 14

oh ok

Answer 15

i got one it's pi/3

Answer 16

yes, and the 2nd one is?

Answer 17

add pi to pi/3

Answer 18

4pi/3

Answer 19

right?

Answer 20

yes

Answer 21

Thanks you so much Dockworker ! :D

Answer 22

those are all solutions in the domain 0<=x<=2pi

Answer 23

Ok

Answer 24

yw