SOLUTION: if cos x°= sin 200° , find the possible values of X between -180° and 360°

Question 1151647: if cos x°= sin 200° , find the possible values of X between -180° and 360°

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
cos(x) = sin(200)
this means that x = arccos(sin(200))
solve for x to get x = 110 degrees.
that's in the second quadrant.
solve for sin(200) to get sin(200) = -.3420201433.
this is negative.
since cos(x) equals this, then cosine is negative.
that would be in the second and third quadrants only.
the equivalent angle in the first quadrant is 180 - 110 = 70 degrees.
the equivalent angle in the third quadrant is 180 + 70 = 250 degrees.
so far you have 110 degrees and 250 degrees.
subtract 360 from these to get equivalent angles of -250 degrees and minus 110 degrees.
since you want angles between -180 and 360 degrees, your solution will be that x = -110 degrees, 110 degrees, and 250 degrees.
to confirm, i graphed the equation of y = cos(x) and y = sin(200).
you can see from this graph that y = arccos(sin(200)) occurs at -180, 110, and 250 degrees when you go between -180 degrees and 360 degrees.

note that y = arccos(sin(200)) is the same as y = arccos(-.342) as shown on the graph.
-.342 shown on the graph is really -.3420201433 rounded to 3 decimal places.

here's the graph.

first graph is the equations used.
second graph is the graph of the equations used.

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