How do you solve for exact value for 0º ≤ x < 360º with the equation #2+sin x = 4-sqrt3/2# ?

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Answer 1 · 2018-02-27T01:03:30

The solutions are #240^@# and #300^@#.

#2+sinx=(4-sqrt3)/2#

#sinx=(4-sqrt3)/2-2#

#sinx=(4-sqrt3)/2-4/2#

#sinx=(4-sqrt3-4)/2#

#sinx=(color(red)cancel(color(black)(4-4))-sqrt3)/2#

#sinx=-sqrt3/2#

Now, we need to find rotations that have a #y#-value of #-sqrt3/2#. Here's a unit circle:

These rotations are #240^@# and #300^@#, so those are the solutions.