SOLUTION: (a) Evaluate the expression under the given conditions. sin(θ/2); tan(θ) = −5/12, θ in Quadrant IV (assume 0 < θ < 2π) (b) Evaluate the expression under the given condi

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Question 1160204: (a) Evaluate the expression under the given conditions.
sin(θ/2); tan(θ) = −5/12, θ in Quadrant IV (assume 0 < θ < 2π)

(b) Evaluate the expression under the given conditions.
tan(2θ); cos(θ) = 3/5, θ in Quadrant I
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
Evaluate the expression under the given conditions.
;
, in Quadrant IV (assume
=>,





, then

and
= ±...since in Quadrant IV, use negative sign







Evaluate the expression under the given conditions.
;
since, , and is given, we have to find
​


, in Quadrant I

-> and
then




so,
then


now we can find
......substitute







Answer by ikleyn(52866)   (Show Source): You can put this solution on YOUR website!
.

            Regarding part  (a),  the solution and the answer by @Mathlover1 are both incorrect;

            therefore, I came to bring the correct solution. 


(a)  if   = -   and   is in QVI, then'


      = ;


       lies in QII, where sine is positive,


     and therefore   = +  =  =  = ,


      totally different formula than solution by @MathLover1.


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