Question 1121172: Find the Value of cosec1395°
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! cosecant (1395) is the same as 1 / sine (1395).
keep subtracting 360 from 1395 until the angle is positive between 0 and 360.
since 1395 / 360 = 3.875, that should take about 3 subtractions.
3 * 360 = 1080.
1395 - 1080 = 315 degrees.
that's in the fourth quadrant.
sine is minus in the fourth quadrant and so is its reciprocal 1 / sine which is equal to cosecant.
so you can expect cosecant (315) to be negative.
consequently, since they're equivalent angles, you can expect cosine (1395) to be negative also.
the equivalent angle to 315 in the first quadrant is equal to 360 - 315 = 45 degrees.
cosecant (45) is equal to 1 / sine (45).
sine (45) is equal to sqrt(2) / 2.
1 / sine (45) is therefore equal to 2 / sqrt(2).
cosecant (45) is therefore equal to 2 / sqrt(2).
since this is equivalent to cosecant (315), which is in the fourth quaedrant, then the cosecant has to be negative.
cosecant (315) which is equivalent to cosecant (1395) is therefore equal to - 2 / sqrt(2).
you can use your calculator to confirm.
1 / sin(1395) is equal to -1.414213562 by the calculator.
- 2 / sqrt(2) is also equal to -1.414213562 by the calculator.
your answer is that the value of cosecant (1395) is equal to -2 / sqrt(2).
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