Use a cofunction to write an expression equal to

csc4π11
.

sin(1/4π11) whatever that means

or
sec(π/2-4π11)

co- means complementary angle.

oops - forget the sin example. Booooguss! I was thinking arcsin.

1/sin(4π11)

To write an expression equal to csc(4π/11), we can use the cofunction identity for sine and cosecant. The cofunction identity states that csc(x) is equal to the reciprocal of sin(x).

since csc(x) = 1/sin(x), we can rewrite csc(4π/11) as:

1/sin(4π/11)

To write an expression equal to csc(4π/11), we can use the cofunction identity for the cosecant function:

csc(x) = 1/sin(x)

Using this identity, we can rewrite the expression as:

csc(4π/11) = 1/sin(4π/11)

Now, to evaluate sin(4π/11), we can use the trigonometric unit circle. The angle 4π/11 radians corresponds to a fraction of the circumference of a circle divided into 11 equal parts.

To determine the value of sin(4π/11), we need to find the y-coordinate of the point on the unit circle that corresponds to the angle 4π/11. By construction, the y-coordinate represents the sine of the angle.

Since 4π/11 radians is not a common angle, we may need to use a calculator or a trigonometric table to find the approximate value of sin(4π/11).