Answer:
Yes!
Step-by-step explanation:
Using the unit circle, we find out that csc(120) = 2/[tex]\sqrt{3}[/tex] and
csc(-120) = - 2/[tex]\sqrt{3}[/tex] . So, -csc(120) = -2/[tex]\sqrt{3}[/tex] .
Note that -120 degrees is actually 240 degrees
The value of cosec(-120) is equal to -cosec(120).
What is trigonometry?
Trigonometry is one of the important branches in the history of mathematics that deals with the study of the relationship between the sides and angles of a right-angled triangle.
According to the given problem,
cosec(x) = [tex]\frac{1}{sin(x)}[/tex]
sin (60) = [tex]\frac{\sqrt{3} }{2}[/tex]
We know, -120° is in the third quadrant, where sine < 0
⇒ cosec ( -120 ) = - sin (60)
⇒ cosec ( -120)
= [tex]\frac{1}{-sin(60)}[/tex]
=[tex]-\frac{1}{\frac{\sqrt{3} }{2} }[/tex]
= [tex]-\frac{2}{\sqrt{3} }[/tex]
Rationalizing the denominator:
= [tex]-\frac{2}{\sqrt{3} }[/tex] × [tex]\frac{\sqrt{3} }{\sqrt{3} }[/tex]
= [tex]-\frac{2\sqrt{3} }{3}[/tex]
= -cosec (120)
Hence, we can conclude, the value of cosec(-120) is -cosec(120).
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