Since csc is the reciprocal of sin, we can first find the value of sin(-3*pi/4) and then take its reciprocal.
To find the value of sin(-3*pi/4), we can use the fact that sin has symmetry about the y-axis. This means that sin(-theta) = -sin(theta) for any angle theta. Therefore, sin(-3*pi/4) = -sin(3*pi/4).
Since 3*pi/4 is in the second quadrant, we can use the unit circle to find its sine. The point on the unit circle that corresponds to 3*pi/4 is (-sqrt(2)/2, sqrt(2)/2), so sin(3*pi/4) = sqrt(2)/2.
Therefore, sin(-3*pi/4) = -sqrt(2)/2.
Taking the reciprocal, we have:
csc(-3*pi/4) = 1/sin(-3*pi/4) = 1/(-sqrt(2)/2) = -sqrt(2)/2.
Find the exact value of the trigonometric function at the given real number
Csc(-3pie/4)
1 answer