How do you solve #tanxsinx-tanx=0# in the interval [0,360]?

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Frenst Share
Feb 20, 2017

Answer:

#tan(x)*sin(x)-tan(x)=0# in the interval #[0;360]# for #x={0;180;360}#

Explanation:

  • Factorize: #tan(x)*sin(x)-tan(x)=0#

#tan(x)*(sin(x)-1)=0#

  • Determinate the domain of the function :

the domain of function #tan(x)# is #RR-{Pi/2+kPi}# with #k in ZZ#
so the domain of function #tan(x)# in the interval #[0;360]# is #[0;90[nn]90;270[nn]270;360]#

the domain of function #sin(x)# is #RR#
so the domain of function #tan(x)# in the interval #[0;360]# is #[0;360]#

so the domain of function #tan(x)*(sin(x)-1)=0# in the interval #[0;360]# is the union of the domain of function #tan(x)# and function #sin(x)-1#
so it's #[0;90[nn]90;270[nn]270;360]#
or in an other way to write it #[0;360]-{90;270}#

  • find the zero of the function in this domain :

#tan(x)*(sin(x)-1)=0# in the interval #[0;360]-{90;270}# when :
- #tan(x)=0# in the interval #[0;360]-{90;270}#
- or #sin(x)-1=0# in the interval #[0;360]-{90;270}#

#tan(x)=0# in the interval #[0;360]-{90;270}# for #x={0;180;360}#

#sin(x)-1=0#
#sin(x)=1# in the interval #[0;360]# for #x={90;270}#
#sin(x)=1# in the interval #[0;360]-{90;270}# for #x=O/#

so #tan(x)*sin(x)-tan(x)=0# in the interval #[0;360]# for #x={0;180;360}#

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