SOLUTION: Find all solutions of the equation in the interval (0,2pi). tan^2x-6tanx+5=0 So far I have: (tanx-1)(tanx-5)=0 tanx=1 and tanx=5 I DO know there will be two solutions. Thank

Question 516222: Find all solutions of the equation in the interval (0,2pi).
tan^2x-6tanx+5=0
So far I have:
(tanx-1)(tanx-5)=0
tanx=1 and tanx=5
I DO know there will be two solutions. Thank you!
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find all solutions of the equation in the interval (0,2pi).
tan^2x-6tanx+5=0
So far I have:
(tanx-1)(tanx-5)=0
tanx=1 and tanx=5
so far everything is correct
to finish:
arctan(-1)=3π/4 and 7π/4 radians (In quadrants II and IV where tan<0
arctan(5)=1.3734 and 4.5134 radians (In quadrants I and III where tan>0
RELATED QUESTIONS
Find all solutions in the interval [0, 2pi) Sec^2x�tanx=... (answered by jim_thompson5910)

Please help! I have already done most of the work. Recently I asked about finding all... (answered by ikleyn)

Solve the equation 4tan^2x + 5 tanx + 1 =... (answered by Alan3354,ikleyn)

find all solutions for tanx=0 for the interval [0,2pi] (answered by lwsshak3)

Hi I have a question about solving trig equations: The equation 2tan^2x+10 tanx+12 can... (answered by Alan3354,stanbon)

I need help solving the following equation for 0(<=) X (<=)2pi tan^2 X +... (answered by Fombitz)

Use inverse functions where needed to find all solutions of the equation in the interval... (answered by ikleyn)

Solve tanx+1=secx and... (answered by Alan3354,Edwin McCravy)

Any help would be much appreciated in figure out this problem. What are all the solutions (answered by MathLover1,math_tutor2020,ikleyn)