Question

find the values of x in the interval [0,2π] |tanx|=1

Answer 1

You can also think of it as: \(\left| \frac{ \sin(x) }{ \cos(x) } \right|\) if it makes it easier

Answer 2

I have to go, so it's x = \(\frac{ \pi }{ 4 }\) and x = \(-\frac{ \pi }{ 4 }\)

Answer 3

how it comes π/4

Answer 4

\[tanx=1 \therefore x= \frac{ \pi }{ 4 } \] in radians, or 45degrees
Test it out on your calculator tan 45

Answer 5

if it is given that

Answer 6

\[0\le x \le 2\pi\] then the answer would be

Answer 7

\[\frac{ \pi }{ 4 } and \frac{ 5\pi }{ 4 }\]
or 45 degrees and 225 degrees

Answer 8

How oit comes 5π/4

Answer 9

is that absolute of tanx=1?

Answer 10

If so \[tanx=\pm1\] since absolute values are always positive regardless of what answer the function provides

Answer 11

between 0 and 2pi
is the same as between 0 and 360degrees when you convert radians into degrees

Answer 12

first of all just find for what values tanx=1
from this we must find the value for which tanx=1/1
for 45degrees opposite side=1 adjacent side=1 therefore tan45=1

Answer 13

here is the part where positive and negative plays its role
since both positive and negative 1 are both answers for \[\left| tanx \right|=1\] we must find the angles for which tanx=+or-1 on the unit circle

Answer 14

Each function is positive in their respective quadrants, with the exception of the first quadrant where every function has a positive outcome. If we were to find tanx=-1 then we would find the angle for the 2nd and 4th quadrant given by
180-45 and
360-45 where the angle is 45 since tan45=1
By doing this you will find the angle for which tanx=-1 which is 135degrees and 315degress

Answer 15

But because we are finding \[tanx=\pm1\] we must find angles for which tan is both 1 and -1, we've already found the angles for -1 now we just have to find the angles for tan=1

Answer 16

using the unit circle we find the angles for tanx=1 in the first and 3rd quadrant

as such the angles would the 45 and
180+45=225