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Optionally, write out the definitions of the Trig functions. Since the answer is provided for you, you're done! Answers: Sin  =  EMBED Equation.3  Cos  =  EMBED Equation.3  Tan  =  EMBED Equation.3  Csc  =  EMBED Equation.3  Sec  =  EMBED Equation.3  Cot  =  EMBED Equation.3   SEQ PartNum \* Arabic 2) Given Sin  =  EMBED Equation.3 , where  is in the second quadrant, with find all the other trig functions using trig identities: There are 5 different functions you need to find. You can do them in any order, and you don't need to do them exactly like this (i.e., there are multiple, valid, ways you can approach these problems) CSC: Reciprocal Identity:  EMBED Equation.3  Substitute the known value in:  EMBED Equation.3  Multiply numerator and denominator by the same value:  EMBED Equation.3  Simplify (denominator goes to 1):  EMBED Equation.3  Simplify (denominator of 1 can be ignored) (This step may be combined with the previous one):  EMBED Equation.3  COS: Pythagorean Identity: Cos2 + Sin2 = 1 Substitute the known value in: Cos2 +  EMBED Equation.3  = 1 Do the exponent: Cos2 +  EMBED Equation.3  = 1 Simplify (Subtraction): Cos2 = 1 -  EMBED Equation.3  Simplify (Common denominator, for subtraction): Cos2 =  EMBED Equation.3  Simplify (Subtraction): Cos2 =  EMBED Equation.3  Square root of each side:  EMBED Equation.3  Simplify (Do the radical)  EMBED Equation.3  Simplify (Do the radical)  EMBED Equation.3  Explain (Via picture or English sentence) that being in Quadrant II means that the cosine is negative SEC: Reciprocal Identity:  EMBED Equation.3  Substitute the known value in:  EMBED Equation.3  Multiply numerator and denominator by the same value:  EMBED Equation.3  Simplify (denominator goes to 1):  EMBED Equation.3  Simplify (denominator of 1 can be ignored) (This step may be combined with the previous one):  EMBED Equation.3  TAN: Quotient Identity:  EMBED Equation.3  (We already know Sin, Cos, so plug those in:  EMBED Equation.3  Multiply numerator and denominator by the same value:  EMBED Equation.3  Simplify: Denominator cancels to 1, and is ignored, cross-cancel on top:  EMBED Equation.3  COT: Reciprocal Identity:  EMBED Equation.3  Multiply each side by Cot, and by  EMBED Equation.3 , in order to get:  EMBED Equation.3  Substitute the known value in:  EMBED Equation.3  Multiply numerator and denominator by the same value:  EMBED Equation.3  Simplify (denominator goes to 1):  EMBED Equation.3  Simplify (denominator of 1 can be ignored) (This step may be combined with the previous one):  EMBED Equation.3  Answers: Sin  =  EMBED Equation.3  Cos  =  EMBED Equation.3<DRTVXZʹtgtUtgH7H h9h CCJ(OJQJ^JaJ(h9h COJQJ^J#h9h2+OJQJ^JmHnHuh9h2OJQJ^J!jh9h2OJQJU^J&h9h8 5>*CJOJQJ^JaJh8 CJOJQJ^JaJ#h8 h8 5CJOJQJ^JaJ h8 h8 CJOJQJ^JaJ h8 5>*CJOJQJ^JaJ hRX5>*CJOJQJ^JaJ&h9h95>*CJOJQJ^JaJVX # T > a H & F$Ifgda $Ifgd&` & F$Ifgd> & F$Ifgd9 $Ifgd:`gdwMlmn$ ( * z     ɶᩛskg\TkgsFsheBh+5OJQJ^Jjh_&UjG h_&UVh_&jh_&UheBh95OJQJ^Jh9h+OJQJ^Jh9h`nOJQJ^Jh9h>*OJQJ^Jh9he7NOJQJ^J%jh9h CEHOJQJU^J/j|G h9h CCJOJQJUV^JaJh9h COJQJ^J!jh9h COJQJU^J ! 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What you hear is the following: "Tangent of 30 degrees? Without using a calculator? No problem. You just draw out your handy-dandy 30-60-90 triangle like this, and notice that the side adjacent to 30 is  EMBED Equation.3 , the opposite is 1, and the hypotenuse is 2. We could just use the definition of tan, namely that tan =  EMBED Equation.3 , but where's the fun in that? Let's use the fact that tan =  EMBED Equation.3 , and that  EMBED Equation.3  (which is  EMBED Equation.3 ), and that cos  =  EMBED Equation.3  (which is  EMBED Equation.3  ). Plug those into the equation for tan, get  EMBED Equation.3 , which simplifies to  EMBED Equation.3  - Voila!" List all the mistakes that Bob has made: (These may be listed in any order) Tangent is  EMBED Equation.3  Sine is  EMBED Equation.3  Cosine is  EMBED Equation.3  Tan is  EMBED Equation.3  Explain why Bob still got the right answer: Basically, Bob's mistakes w/ Sin & Cos 'canceled out' the mistakes with Tan: Some math might illustrate this better: According to Bob, tan =  EMBED Equation.3 . Plugging in what Bob thinks is cos & sin, we get  EMBED Equation.3 . Ignore the 1 in the denominator, and multiply top & bottom by , and get  EMBED Equation.3 . This just happens to be the same values we get if we plug in the correct values of sin ( EMBED Equation.3 ) and cos ( EMBED Equation.3 ) into the correct identity for tan ( EMBED Equation.3 , or  EMBED Equation.3 ), which then simplifies to  EMBED Equation.3 , or  EMBED Equation.3 .     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