Question

tan^2x+tanx=0

Answer 1

For these types of problems factor them out, since we cant factor completely we can pull out a Tan(x) so we can get, Tan(x) (Tan(x)+1) = 0 now set each of these equal to zero to solve.
Tan(x) = 0 Tan(x) +1 =0
Can you get it from here?

Answer 2

no lol i have no idea what to do with this trig stuff

Answer 3

that's play it's why we are here.
well Tan(x) = 0 that is the first one and the easiest. We need to look at our unit circle and find out where tan(x) is = to 0 which if you look is anywhere where sin(x) is =0 so , 0 and pi
For tan(x) +1= 0 well make Tan(x) =-1 and do the same thing
well again looking at the unit circle we know that anywhere pi/4 tan(x) is =1 follow me so far?

Answer 4

okay*

Answer 5

yes

Answer 6

so tan= -1 would just be pi?

Answer 7

actually no 3pi/2

Answer 8

no not quite, if we know that pi/4 is either 1, -1 its going to be either pi/4 3pi/4 5pi/4 or 7pi/4

Answer 9

its going to be some variation of pi/4 because tangent is sine over cosine, for tangent to be 1, cosine and sine need to be equal which occurs at pi/4, 3pi/4, 5pi/4 and 7pi/4

Answer 10

well we know, quadrant 1 coordinates are (+,+) so tangent would be +/+ = + so its not in quadrant 1
quadrant 2 coordinates are (-,+) which if we do tangent is +/- = - so quadrant 2 is valid
quadrant 3 is (-,-) so -/- = +so quadrant 3 cant be it
quadrant 4 is (+,-) so a -/+ = a -
so for tangent of x to be a -1 it has to be in quadrant 2 and 4 to be negative and a pi/4 variation to be a one

Answer 11

so we find the pi/4 in quadrant 2 and 4 and the answer should be 3pi/4 and 7pi/4 along with your earlier answers of 0 and pi
Answers: (0,3pi/4,pi,7pi/4)

Answer 12

these ansers dont have to be added to Kpi?

Answer 13

it depends on the question if it says for the interval [0,2pi] then no, but if it says all values then yes just put all of them in parentheses and put +2kpi

Answer 14

yes its {0, 2pi] thanks for your help!

Answer 15

yep!

Answer 16

i have 2 other questions that im stumped on if you can help

Answer 17

sin2x-sinx+2cosx-1=0

Answer 18

sin2x-sinx+2cos=1