Math, asked by pankajk09127, 11 months ago

find the value of sin(-1740)​

Answers

Answered by Theboss0184
0

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

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