SOLUTION: If csc (theta) <0 and cos(theta)=5/13, find sin (theta/2) and cos (theta/2).

Question 1076776: If csc (theta) <0 and cos(theta)=5/13, find sin (theta/2) and cos (theta/2).
Answer by ikleyn(52786) (Show Source): You can put this solution on YOUR website!
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If csc (theta) <0 and cos(theta)=5/13, find sin (theta/2) and cos (theta/2).
~~~~~~~~~~~~~~~~~~~~~~~~

 <  means  < .

Together with  = , it means that  is the angle in QIV.

Hence,   is the angle in QII.


Then   =  =  =  =  =  = .

The sign is "+" since sine is positive in QII.


 =  =  =  =  =  = .

The sign is "-" since cosine is negative in QII.

To see more solved similar problems on calculating trig functions look into the lessons
    - Calculating trigonometric functions of angles
    - Advanced problems on calculating trigonometric functions of angles
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Trigonometry: Solved problems".

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