In which quadrants do cosine and tangent have the opposite sign?

Question

6488 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-06T11:55:36

#bb(III)# and #bb(IV)#

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)# and #bb(IV)#

Answer 2 · 2018-03-06T12:12:42

#color(blue)(III , IV ) # quadrants.

enter image source here

From the above table one can deduce trigonometric functions cosine & tangent have opposite signs in III & IV quadrants