To find the exact value of the real number y = csc(1), we start by recalling that cosecant is the reciprocal of the sine function. Thus, we have:
csc(x) = 1/sin(x)
Therefore, we can express y as:
y = csc(1) = 1/sin(1)
Next, we need to evaluate sin(1). The angle is in radians, and using a calculator, we find:
sin(1) ≈ 0.84147
Now, substituting this back into our equation, we get:
y ≈ 1/0.84147 ≈ 1.1884
Thus, the exact value of y = csc(1) in decimal form can be approximated as:
y ≈ 1.1884
In conclusion, we’ve established that the value of y as csc(1) is the reciprocal of the sine of 1 radian, providing an approximate numerical result.