# If Sin theta = 5/13, theta in quadrant II, how do you find the exact value of each of the remaining trigonometric functions of theta?

Aug 20, 2016

$\sin \theta = \frac{5}{13} \text{ "cos theta = -12/13" } \tan \theta = \frac{5}{-} 12$

$\cos e c \theta = \frac{13}{5} \text{ "sec theta = 13/-12" } \cot \theta = - \frac{12}{5}$

#### Explanation:

$\sin \theta$ is defined as $\left(\text{opposite")/("hypotenuse}\right)$ or on a Cartesian grid, $\sin \theta = \frac{y}{r}$

The sides of the right-angled triangle in this case are $5 , 12 , 13$

HOwever, in Quadrant ll, the x-values are negative, (-12)

The values of the 6 trig ratios in the second quadrant will be:

$\sin \theta = \frac{5}{13} \text{ "cos theta = -12/13" } \tan \theta = \frac{5}{-} 12$

$\cos e c \theta = \frac{13}{5} \text{ "sec theta = 13/-12" } \cot \theta = - \frac{12}{5}$