Question 596838
Hi, there--
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You first need to find the measure of a congruent angle with a degree measure between 0 degrees and 360 degrees (an angle less than or equal to one rotation around the unit circle.) You find this by adding an integer multiple of 360 to -675 degrees to give a value in that range. In this case we add 2*360=720 
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{{{-675+(2*360)=-675+720=45}}}
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An angle with a measure of -675 degrees is congruent to an angle with a measure of 45 degrees.
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45 degrees is one of those benchmark values in trigonometry. You should recognize right away that 
{{{sin(45)=sqrt(2)/2}}}
{{{cos(45)=sqrt(2)/2}}}
{{{tan(45)=1}}}.
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That's it. Feel free to email me via gmail if my explanation is unclear.
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Ms.Figgy
math.in.the.vortex@gmail.com