Question

Three trigonometric functions for a given angle are shown below. Cosecant theta equals 13/12 secant Theta equals -13/5, cotangent equals -5/12. Where are the coordinates of point (x,y) On the terminal ray of angle theta assuming that the values above not simplified ?

Answer 1

Answer:

(-5/12) A on edg

Step-by-step explanation:

Answer 2

$\bf cot(\theta)=\cfrac{adjacent}{opposite} \qquad % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} \qquad % secant sec(\theta)=\cfrac{hypotenuse}{adjacent}\\\\ -------------------------------\\\\ csc(\theta)=\cfrac{13}{12}\cfrac{\leftarrow hypotenuse=r}{\leftarrow opposite=y}\qquad sec(\theta)=\cfrac{13}{-5}\cfrac{\leftarrow hypotenuse=r}{\leftarrow adjacent=x} \\\\\\ cot(\theta)=\cfrac{-5}{12}\cfrac{\leftarrow adjacent=x}{\leftarrow opposite=y}$

the hypotenuse, or "r" radius, is just a unit length, thus is never negative, so, if the fraction is negative, is not due to the hypotenuse, is due to the other component, so, in the case of -13/5, the 13 can't be negative, so it has to be the 5 that makes the fraction negative, thus the adjacent side is -5.