SOLUTION: Name the quadrants in which angle theta may lie if sec(<font face="symbol">q</font>) = csc(<font face="symbol">q</font>).

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Question 423187: Name the quadrants in which angle theta may lie if sec(q) = csc(q).
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!


                        Signs
Quadrant        I    II    III    IV 
--------------------------------------
Sine            +     +     -      -
Cosine          +     -     -      +
Tangent         +     -     +      -
Cotangent       +     -     +      -
Secant          +     -     -      +
Cosecant        +     +     -      -
--------------------------------------

The Secant and the Cosecant are both POSITIVE in quadrant I 
The Secant and the Cosecant are both NEGATIVE in quadrant III

So the answer is quadrants I and III since to be equal they
must have the same sign.  

If you want to know what these angles are,

In degrees 

 sec(45°+360°n) = csc(45°+360°n)
sec(225°+360°n) = csc(225°+360°n)

In radians 

 sec(p/4+2np) = csc(p/4+2np)
sec(5p/4+2np) = csc(5p/4+2np)

Edwin
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