csc -5pi/6 =
is it -2?
sin 5 pi/6 = sin 150 degrees = -sin 30 = -1/2
csc = 1/sin so yes, it is -2
To determine the value of csc(-5π/6), we can use the reciprocal identity of the sine function. The reciprocal of sine is csc (cosecant) and can be calculated as 1/sin(x).
First, let’s find the value of sin(-5π/6).
The sine function for -5π/6 radians can be evaluated by considering the unit circle. In the unit circle, -5π/6 radians corresponds to a point on the circle’s terminal side that is 5/6 of a full revolution (or 150 degrees) clockwise from the positive x-axis.
At 5/6 of a full revolution clockwise, the corresponding y-coordinate is -1/2, which is the sine of -5π/6.
So, sin(-5π/6) = -1/2.
Now, let’s calculate csc(-5π/6) using the reciprocal identity:
csc(-5π/6) = 1/sin(-5π/6) = 1/(-1/2) = -2.
Therefore, csc(-5π/6) is indeed equal to -2.
So, your initial guess of -2 is correct!