Answer:
(–5, 12) is the correct answer.
Step-by-step explanation:
We are given the following values:
[tex]cosec\theta = \dfrac{13}{12}\\sec\theta=-\dfrac{13}{5}\\cot\theta =-\dfrac{5}{12}[/tex]
Now, we know the following identities:
[tex]sin \theta = \dfrac{1}{cosec\theta}\\cos \theta = \dfrac{1}{sec\theta}\\tan \theta = \dfrac{1}{cot\theta}[/tex]
Now, the values are:
[tex]sin\theta = \dfrac{12}{13}\\cos\theta=-\dfrac{5}{13}\\tan\theta =-\dfrac{12}{5}[/tex]
Sine value is positive and cos, tan values are negative.
It can be clearly observed that [tex]\theta[/tex] is in 2nd quadrant.
2nd quadrant means, the value of [tex]x[/tex] will be negative and [tex]y[/tex] will be positive.
Let us have a look at the value of [tex]tan\theta[/tex]:
[tex]tan\theta = \dfrac{Perpendicular}{Base}\\OR\\tan\theta = \dfrac{y-coordinate}{x-coordinate} = -\dfrac{12}{5}\\\therefore y = 12,\\x = -5[/tex]
Please refer to the attached image for clear understanding and detailed explanation.
Hence, the correct answer is coordinate (x,y) is (–5, 12)
