3pi/4 is a solution to tan(x) = -1.
I'm working on a few problems where I have to figure out all solutions to a given equation between [0,2PI). Here's one i got but i'm not all that sure that it is correct:
tan x ^ 2 - 2 tan x - 3 = 0
My Solution:
(tan x - 3) (tan x + 1) = 0
tan x = 3 , tan x = -1
Both have no solution.
I don't think this is right though, i've yet to solve any of these problems where i didn't find at least one solution. I'm guessing i would probably have to solve it another way correct?
Hello, MajorJohnson!
Find all solutions on [0, 2pi]
. . (tan x)^2 - 2(tan x) - 3 .= .0
My Solution:
. . (tan x - 3)(tan x + 1) .= .0
. . tan x =3 . . . tan x = -1
Both have no solution. . What?
Did you try your calculator?
. . x .= .arctan(3) .≈ .0.40(pi)
. . x .= .arctan(-1) .= .0.75(pi)
Two comments....first is your calculator in degree or radian mode? Also Soroban is giving his answers in terms of multiples of pi. To get his answer for atan(-1), for example, plug in atan(-1) to get -0.785398, then divide by pi = 3.1415927. You will get -0.25. I'll let you figure out how Soroban got 0.75. (Hint: Think about what quadrant the angle -1 rad is in.)
-Dan
Question: Why did you divide by PI?
I was able to get that answer by doing what you described above.
Tan 3 is in quadrant 1 and 3.
so plugging in Tan (3) will give me -.14254... and i'll divide that by PI to give me -.04537...
So following your previous post:
Why did you divide by PI?
Tan 3 would be in in quadrant 1 and 3.
so plugging in Tan (3) will give me -.14254... and i'll divide that by PI to give me -.04537...
But i still think that tan 3 would be present no solution because it is greater than 1. So the answer in radians would just be
3PI/4 and 7PI/4 right?
Posts # 2 and #3 gave you most of the answer. Below are all the solutions. You need to become more familiar with the symmetry of the unit circle, as well as the tan function. I suggest you thoroughly revise that material.
7 pi/4 is another.
And the solution to tan(x) = 3 is x = arctan(3) or x = pi + arctan(3).