Question 1197786

In Quadrant I, {{{cos(theta) > 0}}}, {{{sin(theta) > 0}}} and {{{tan(theta) > 0}}} (All positive).

 In Quadrant II, {{{cos(theta) < 0}}}, {{{sin(theta) > 0}}} and {{{tan(theta) < 0 }}}(Sine positive).

 In Quadrant III, {{{cos(theta) < 0}}}, {{{sin(theta) < 0 }}}and {{{tan(theta) > 0}}} (Tangent positive).

In Quadrant IV, {{{cos(theta) > 0}}}, {{{sin(theta) < 0}}} and {{{tan(theta) < 0}}} (Cosine positive).


so,

{{{tan(theta) > 0}}} in quadrant I,  III
Secant is reciprocal of cosine which is negative in the II and III quadrant, so 
{{{sec(theta)< 0}}} in quadrant II,III


answer is: C. III