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How do you solve this trigonometric equation?

Find the solutions to the equation

#2##sin##theta##cos##theta##-##sin##theta# = #0#

#-180##<=##theta##<=##180#

Answer 1

Josiah Anderson

#theta=-180^@,-60^@,0^@,60^@,180^@#

#2sinthetacostheta-sinteta=0#

#=>sintheta(2costheta-1)=0#

therefore either #sintheta=0# i.e. in the given interval #-180^@<=theta<=180^@#, we have #theta=-180^@,0^@,180^@#

or #2costheta=1# i.e. #costheta=1/2# and #theta=-60^@,60^@#

Hence #theta=-180^@,-60^@,0^@,60^@,180^@#

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Answer 2

James Adkins

To provide the most accurate guidance, I'll need to know the specific trigonometric equation you'd like assistance with. Could you please provide the equation you're referring to?

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

How do you solve this trigonometric equation?

Find the solutions to the equation #2##sin##theta##cos##theta##-##sin##theta# = #0# #-180##<=##theta##<=##180#

Find the solutions to the equation

#2##sin##theta##cos##theta##-##sin##theta# = #0#

#-180##<=##theta##<=##180#