Solve the equation on the interval [ 0 , 2 π ] tan ⁡ 2...

Nathalie Fields

Nathalie Fields

Answered

2022-07-25

Solve the equation on the interval [ 0 , 2 π ]
tan 2 x tan x = 0

Answer & Explanation

Izabelle Frost

Izabelle Frost

Expert

2022-07-26Added 13 answers

We then divide tan 2 x and tan x by what has been taken out or tan x.
After factoring, we get this trig equation in factored form:
tan x ( tan x 1 ) = 0
We have two factors and they are:
tan x and tan x 1
Set each factor to zero just like you did in algebra 1 andsolve for the given trig function.
tan x = 0
When does tan x = 0?
tan x = 0 at 0 degrees (the same as 360 degrees) and 180 degrees.
We now set the other factor to 0 and solve the equation.
tan x 1 = 0
Adding 1 to both sides we get:
tan x = 1
When does tan x = 1?
tan x = 1 at 45 degrees and 225 degrees
All degrees between the given interval are: 0 degrees (or 360degrees), 180 degrees, 45 degrees and 225 degrees.
If you want the answer in radians, here is it:
All radian measures are:
π 4 , π , 5 π 4 , and 2 π
valtricotinevh

valtricotinevh

Expert

2022-07-27Added 3 answers

tan 2 x = 2 tan ( x ) 1 tan 2 ( x )
2 tan ( x ) 1 tan 2 ( x ) tan ( x ) 1 tan 2 ( x ) = 0
2 tan ( x ) tan ( x ) ( 1 tan 2 ( x ) ) 1 tan 2 ( x ) = 0
2 tan ( x ) tan ( x ) + tan ( x ) tan 2 ( x ) = 0
tan ( x ) + tan ( x ) tan 2 ( x ) = 0
tan ( x ) ( 1 + tan 2 ( x ) ) = 0
tan ( x ) = 0 or tan 2 ( x ) = 1
x = 0 or 2 π

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