What are all the options for x in 2tanx=3sinx?

1 Answer
Hriman
May 8, 2018

#x= 0+pin#
#x=0.841 +2pin#
#x=-0.841 +2pin#

#n# is an element of all integers

Explanation:

#2tanx=3sinx#

#2tanx-3sinx=0#

#sinx(2secx-3)=0#

#sinx=0#
#x= 0, pi#
#x= 0+pin#

#secx=3/2#

Reciprocate both sides:
#cosx=2/3#

#x= arccos(2/3)=0.841 +2pin#

Arccosine leaves out the possible solution in quadrant four so that can be found by, (HINT: DRAW A TRIANGLE IN THE FOURTH TRIANGLE AND SOLVE FOR THE OPPOSITE LEG):

#x= arcsin(-sqrt5/3)= -0.841 +2pin#

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