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
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?
Yes, thank you!
