How to solve #4sintheta=3cosectheta# if #0<x<360#?

The answer is #theta=60, 120, 240 and 300# degrees, but I can only find the answer #theta=60, 120# degrees, for some reason.

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1 Answer
Lucy
May 15, 2018

Below

Explanation:

#4sintheta=3cosectheta#

#4sintheta=3/sintheta#

#4(sintheta)^2=3#

#(sintheta)^2=3/4#

#sintheta=+-sqrt(3/4)#

#sintheta=+-(sqrt3)/2#

#sintheta=(sqrt3)/2# or #sintheta=-(sqrt3)/2#

#theta=60,120,240,300#

A common mistake is that when you square root a number, you always have to make sure you have the #+-# in front because if you square a positive or negative number, both will end up having a positive answer

ie #(-2)^2=4# and #2^2=4#

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