# How do you find the two quadrants that theta could terminate given sintheta=-3/sqrt10?

May 13, 2017

$\text{third and fourth}$

#### Explanation:

$\text{for " 180^@ < theta < 0^@" that is first/second quadrants}$

$\text{then " sintheta" has a "color(blue)"positive value}$

$\text{for " 360^@ < theta < 180^@" that is third/fourth quadrants}$

$\sin \theta \text{ has a "color(blue)"negative value}$

$\text{since } \sin \theta = - \frac{3}{\sqrt{10}}$

$\text{then "theta" will terminate in the third or fourth quadrant}$

$\text{the acronym " ASTC" indicates which ratio is "color(red)"positive}$
$\text{in the relevant quadrant}$

$A \text{ indicates All trig ratios in first quadrant}$

$S \text{ indicates Sine ratio in second quadrant}$

$T \text{ indicates Tangent ratio in third quadrant}$

$C \text{ indicates Cosine ratio in fourth quadrant}$