In which quadrants do cosine and tangent have the opposite sign?
Risposta:
#bb(III)# e #bb(IV)#
Spiegazione:
Starting from the initial side, #theta=0# and rotating counter- clockwise through each quadrant, we have:
#color(white)(888888888)bbIcolor(white)(8888888)bb(II)color(white)(8888888)bb(III)color(white)(8888888)bb(IV)#
#bb(cos(theta)##color(white)(88)bb(+)color(white)(888.88)-color(white)(888.888)-color(white)(8888.88)+#
#bb(tan(theta)##color(white)(88)bb(+)color(white)(888.88)-color(white)(888.888)+color(white)(8888.88)-#
From this we can see that they have opposite signs in quadrants.
#bb(III)# e #bb(IV)#