Question

evaluate cosec (-1410)

Answer 1

First convert the angle given in degree to radian.
−1410°=−1410(π/180)=−(47/3)π=−(8–1/6)π−1410°=−1410(π/180)=−(47/3)π=−(8–1/6)π
So,
cosec(−1410°)=cosec(−8–1/6π)cosec(−1410°)=cosec(−8–1/6π)
cosec(−x)=−cosec(x)cosec(−x)=−cosec(x), then:

cosec(−1410)=−cosec(8–1/6π)cosec(−1410)=−cosec(8–1/6π)

cosec(−1410)=−cosec(8-1/6π)cosec(−1410)=−cosec(8–1/6π)

As we know that after an interval of 2π, values ofcoseccosecrepeat. Then:

cosec(−1410)=−cosec(8–1/6π)cosec(−1410)=−cosec(8–1/6π)

cosec(−1410)=−cosec(–1/6π)cosec(−1410)=−cosec(–1/6π)

cosec(−1410)=cosec(1/6π)cosec(−1410)=cosec(1/6π)

cosec(−1410)=cosec(30°)cosec(−1410)=cosec(30°)

cosec(−1410)=1/sin(30°)cosec(−1410)=1/sin(30°)

cosec(−1410)=1/(1/2)cosec(−1410)=1/(1/2)

cosec(−1410)=2cosec(−1410)=2

Is the solution.

Hope It Helps! :-)