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

Mar 6, 2018

$\boldsymbol{I I I}$ and $\boldsymbol{I V}$

#### Explanation:

Starting from the initial side, $\theta = 0$ and rotating counter- clockwise through each quadrant, we have:

$\textcolor{w h i t e}{888888888} \boldsymbol{I} \textcolor{w h i t e}{8888888} \boldsymbol{I I} \textcolor{w h i t e}{8888888} \boldsymbol{I I I} \textcolor{w h i t e}{8888888} \boldsymbol{I V}$

bb(cos(theta)$\textcolor{w h i t e}{88} \boldsymbol{+} \textcolor{w h i t e}{888.88} - \textcolor{w h i t e}{888.888} - \textcolor{w h i t e}{8888.88} +$

bb(tan(theta)$\textcolor{w h i t e}{88} \boldsymbol{+} \textcolor{w h i t e}{888.88} - \textcolor{w h i t e}{888.888} + \textcolor{w h i t e}{8888.88} -$

From this we can see that they have opposite signs in quadrants.

$\boldsymbol{I I I}$ and $\boldsymbol{I V}$

Mar 6, 2018

$\textcolor{b l u e}{I I I , I V}$ quadrants.

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