Question

Find the exact value of csc (1020 °).

Find the exact value of csc (1020 °).
Math   Precalculus   
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Answer #1

Remove full rotations of 360 degree until the angle is between 0 and 360 degrees.

csc(300)

By applying simple reference angle, we can calculate the value for the csc(300) as csc(360 - 60), which lies in the fourth quadrant.

Therefore, it will become -csc(60)

The exact value of csc(60) is 2 / sqrt(3), and for -csc(60) it will become - 2 / sqrt(3).

In order to find the more precise answer we can rationalise the value by multiplying both numerator and denominator by sqrt(3).

Finally, the value will become -2(sqrt(3)) / 3.

The decimal value is: -1.154

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