Question

solve (0,2pi]
2 cos x tan x +square3 tan x =0
:( help

Answer 1

between both terms, tan x is common.

So factor out tan x.

Answer 2

\[\tan x (2 \cos x +\sqrt{3})\]

Answer 3

Great. Now set each factor equal to 0.

Answer 4

tanx=0
cosx = -\[\sqrt{3/2}\]

Answer 5

- sqrt(3)/2

Answer 6

now find the angles x that satisfies each equation.

Answer 7

cosx = \[5\pi/6 , 7\pi/6\]

Answer 8

great! what about tan x = 0?

Answer 9

tanx = cos/sin

Answer 10

dont go that route

Answer 11

you should know, that tan 0 = 0; tan 180 = 0, tan 360 = 0

Answer 12

but you dont want to include 0 as the directions say (0,360]

Answer 13

right

Answer 14

Look at the tan x graph

Answer 15

you can see from the graph that tan 0 = 0; tan 180 (pi) = 0; tan 360 (2 pi) = 0

Answer 16

yes

Answer 17

So you have 4 solutions to the equation.

Answer 18

5pi/6, 7pi/6 , 0

Answer 19

No...we said that 0 is not to be included. You need to include pi and 2 pi. (thats where tan x = 0)

Answer 20

pi and 2pi

Answer 21

yes

Answer 22

you understand why we are excluding 0 for this problem?

Answer 23

i'm

Answer 24

huh?

Answer 25

i understand

Answer 26

thanks for you time :)