All six trigonometric ratios were calculated using a unit circle and comes out to be
[tex]sin(-\pi )= -sin\pi =0\\cos(-\pi )= cos\pi =-1\\tan(-\pi )= -tan\pi=0 \\cosec(-\pi )= -cosec\pi =infinity\\sec(\pi )= sec\pi =-1\\cot(-\pi )=-cot\pi=infinity[/tex]
I have attached a unit circle diagram.
What is a unit circle in trigonometry?
In this unit circle corresponding values of sine and cosine have been written near the angle 'α' in form (cosα,sinα)
x-coordinate is cosα
y-coordinate is sinα
now,
one can find other trigonometric ratios
[tex]tan\alpha =\frac{sin\alpha }{cos\alpha } \\\\cot\alpha =\frac{1}{tan\alpha } \\\\cosec\alpha =\frac{1}{sin\alpha } \\\\sec\alpha =\frac{1}{cos} \\[/tex]
Hence, we can find the rest of the trigonometric ratios by using the coordinates (cosα,sinα) for a particular angle 'α'.
to get more about unit circle refer to the link,
https://brainly.com/question/16577559
