How do you solve the equation #tan^2theta-tantheta-2=0# for #0^circ<=theta<360^circ#?

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Answer 1 · 2016-12-07T10:06:06

The answer is #theta={63.4º,243.4º,315º,135º}#

You solve this like a quadratic equation

#ax^2+bx+c=0#

Where #x=tantheta#

We calculate #Delta=b^2-4ac#

#=(-1)^2-4*(1)*(-2)#

#=1+8=9#

So,

#Delta>0#, we have 2 real roots

#x=(-b+-sqrt(Delta))/(2a)#

#tantheta=(1+-sqrt9)/2=(1+-3)/2#

#Tan theta=2# and #tantheta=-1#

and #0<=theta<360#

#theta={63.4º,243.4º,315º,135º}#