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I need to use algebra to solve this equation over the domain 0° ≤ x < 360°. Give the roots to the nearest degree where necessary.

 

sec x = \({-1 \over 2}\) csc x

 Jun 3, 2020
 #1
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sec(x)  =  1/cos(x)          csc(x)  =  1/sin(x)

 

           sec(x)  =  -½·csc(x)

    [ 1/cos(x) ]  =  -½ · [ 1/sin(x) ]                       ( make the trig substitutions )

sin(x) / cos(x)  =  -½                                         ( multiply both sides by sin(x) )

            tan(x)  =   -½                                        ( tan(x)  =  sin(x) / cos(x) )

                   x  =  tan-1(  -½ )

 

Can you finish?

 Jun 3, 2020
 #2
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Yes, thank you!

Guest Jun 3, 2020

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