find the value of sin(-1740)
Answers
Answer:
Consider \csc (-1740^{\circ})csc(−1740
∘
)
We know that angle -\theta−θ lies in fourth quadrant and \csc(-\theta )csc(−θ) is negative in the fourth quadrant .
So, \csc (-1740^{\circ})=-\csc(1740^{\circ} )csc(−1740
∘
)=−csc(1740
∘
)
We can write 1740^{\circ}1740
∘
as 1740^{\circ}=10\pi-60^{\circ}1740
∘
=10π−60
∘
Therefore,
\begin{gathered}\csc (-1740^{\circ})=-\csc(1740^{\circ} )=-\csc ( 10\pi-60^{\circ} )\\\csc(-\theta )\end{gathered}
csc(−1740
∘
)=−csc(1740
∘
)=−csc(10π−60
∘
)
csc(−θ)
Here, 10\pi-60^{\circ}10π−60
∘
lies in fourth quadrant in which cosec function is negative, so \begin{gathered}\csc (-1740^{\circ})=-\csc(1740^{\circ} )=-\csc ( 10\pi-60^{\circ} )\\\csc(\theta )=\csc ( 60^{\circ} )=\frac{2}{\sqrt{3}}\end{gathered}
csc(−1740
∘
)=−csc(1740
∘
)=−csc(10π−60
∘
)
csc(θ)=csc(60
∘
)=
3
2