I'm trying to find the cosecant of 11 pi/6. The answer is -2, but I'm not sure where this came from. I thought You would flip the sine value which was sq. root of 3/2, making it 2/sq. root of three, which would then become sq. root of -6 over 3 or sq. root of -2. Why isn't there a sq. root sign? Thanks!!!

11pi/6 is just pi/6 short of 2pi

so csc 11pi/6
= csc (-pi/6)
= -csc pi/6
= -1/sin pi/6
= -1/(1/2), [sin 30º = sin pi/6 = 1/2]
= -2

I don't understand the math please

I don't understand the math please .
I don't understand the math please.

To find the cosecant of an angle, you are correct that you would typically take the reciprocal of the sine value of that angle. However, it seems there is an error in your calculations.

Given the angle 11π/6, we can determine its reference angle (an angle in the first quadrant with the same sine value) by subtracting the angle from π. In this case, the reference angle is π - 11π/6 = π/6.

Now, let's find the sine of the reference angle. The sine of π/6 is 1/2.

To find the cosecant, we take the reciprocal of the sine value. So, the cosecant of π/6 is 1 / (1/2) = 2.

Therefore, the cosecant of 11π/6 is 2, not -2.The mistake in your calculation might be related to the incorrect sign you introduced when taking the reciprocal.

To find the cosecant of 11π/6, we need to understand a few trigonometric concepts. Firstly, the cosecant function (csc) is the reciprocal of the sine function (sin). So, to find csc(11π/6), we can start by finding sin(11π/6) and then take its reciprocal.

To evaluate sin(11π/6), let's first identify the reference angle. The reference angle is the acute angle formed between the terminal side of the angle and the x-axis in standard position.

In this case, 11π/6 is in the fourth quadrant, as it is greater than 2π (360 degrees) but less than 3π/2 (270 degrees). To find the reference angle, we subtract the nearest complete revolution, which is 2π.

11π/6 - 2π = (11π - 12π)/6 = -π/6

Now, we have our reference angle as -π/6. The sine of -π/6 is defined as the y-coordinate of the point on the unit circle corresponding to the angle. In this case, the point (-1/2, -√3/2) lies on the unit circle and corresponds to the angle -π/6.

So, sin(-π/6) = -√3/2

Now, to find the cosecant of -π/6 (csc(-π/6)), we take the reciprocal of sin(-π/6):

csc(-π/6) = 1 / sin(-π/6) = 1 / (-√3/2)

To rationalize the denominator, we multiply both the numerator and denominator by √3:

csc(-π/6) = (1 * √3) / (-√3/2 * √3) = √3 / (-√3 * 2) = √3 / (-2√3)

simplify:

csc(-π/6) = -1/2

So, the correct answer is -1/2, not -2.

It seems there was an error in your calculations. To find the reciprocal of sine, you do not put a square root sign in the denominator. The correct reciprocal is -1/2, not -2.