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

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

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.

Answer 2

In this exercise we have to use the knowledge of triangles to calculate the value of the angle, we have to:

$\theta=-1$

Knowing that the cotangent formula is given by:

$cot(\theta)=adj/opp$

Gathering some information given in the text we have that:

• $cossecant(\theta)=13/12$
• $secant(\theta)=-13/12$
• $cotangent(\theta)=-13/5$

We know that no size can be negative so we have the adjacent side is just 5.

See more about angles at brainly.com/question/15767203