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

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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.

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