SOLUTION: Find all solutions to the equation on the interval [0,2pie) cos(2theta)-tan(theta)=1
Here is my work: *=theta
cos(2*)-tan(*)-1=0
1-2sin^2(*)-sin(*)/cos(*)-1=0
cos(*)-2sin^2(*
Algebra.Com
Question 78336: Find all solutions to the equation on the interval [0,2pie) cos(2theta)-tan(theta)=1
Here is my work: *=theta
cos(2*)-tan(*)-1=0
1-2sin^2(*)-sin(*)/cos(*)-1=0
cos(*)-2sin^2(*)cos(*)-sin(*)-cos(*)=0
-2sin^2(*)cos(*)-sin(*)=0
-Sin(*)[2sin(*)cos(*)-1]=0
-sin(*)=0 2sin(*)cos(*)=0
-(*)=-pie/2,-3pie/2 sin(*)=0 cos(*)=0
(*)=pie/2,3pie/2 (*)=pie, 2pie
Did I do this correctly?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You're right so far, but lets look at this step "-2sin^2(*)cos(*)-sin(*)=0"
[-2sin(\theta)cos(\theta)-1]=0)
Factor out a )
=0)
Set the first term equal to zero
Take the arcsine of both sides
So for this solution you should have
(if we let n=0), 
(if we let n=1)
Now let cos(\theta)-1)
equal zero
cos(\theta)-1=0)
-1=0)
Replace cos(\theta))
with )
=1)
Add 1 to both sides
Take the arc sine of both sides
Divide both sides by -2
So just looking in the interval [0,
) (excluding ) we get the solutions
Let n=1
Let n=2
So we only have 4 solutions in the interval [0,):
, 
, , 
RELATED QUESTIONS
find two solutions in the interval 0 degrees (answered by Fombitz)
Use the given information to find sin 2theta, cos 2theta, and tan 2theta.
#1) cos theta (answered by lwsshak3)
Solve the interval 0 (answered by Fombitz)
find all solutions of the equation tan^2theta=3/2sec theta in the interval [0,... (answered by lwsshak3)
sin theta= 12/13, 3pi/2 (answered by Edwin McCravy,feliz1965)
Solve the equation for solutions over the interval [0, 360). Give solutions to the... (answered by Fombitz)
cos^2theta-sin^2theta/cos^2theta+sin theta cos theta=1-tan... (answered by greenestamps)
Solve the equation on the interval: O < or equal to Theta < 2 pi.
Tan(2Theta) =... (answered by stanbon)
Find the solution, if possible.
{{{(1 +... (answered by Edwin McCravy)