William W. answered • 07/03/19
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Based on your situation, assuming you do NOT wish to relearn the unit circle (which I believe is a mistake, BTW), perhaps the best way is to just use your calculator and the rule that tangent (and cotangent) repeat every 180°.
To use your calculator, to find the angle where the tangent is a given number, you would use the tan-1 button (usually its the "2nd function" "tan" button). In this case, type into your calculator tan-1(-1) and you will probably get -45° (that's what my TI-84 Plus CE says anyway). Now you have to realize that -45° is the same as 315° and they are both the same as 7pi/4 (separate discussion). Now, use the rule that tangent repeats every 180° (or pi radians) to back off from 7pi/4 by pi radians (aka 4pi/4) to get 3pi/4 (7pi/4 - 4pi/4 = 3pi/4). So the answer is H.
Arthur D.
07/03/19
William W.
All the trig functions are cyclical meaning they repeat after a certain period. Sine and cosine repeat every time you make a complete loop around the circle but tangent is different and repeats every half loop around the circle (180 degrees or pi radians). Tangent is actually sine divided by cosine so the result is that it repeats more often.07/03/19
Matthew Y.
By far the best answer, but can you explain the rule at the end (that tangent repeats every 180? And why is -45 the same as 315? Thanks for reading07/03/19