Final answer:
The exact value of csc²(300°) is calculated using the relationship csc(θ) = 1 / sin(θ), and knowing that sin(300°) = -√3/2, the result is 4/3.
Step-by-step explanation:
To calculate the exact value of cosecant squared (csc²) for an angle of 300°, we can use the trigonometric identity that relates it to the sine function:
csc(θ) = 1 / sin(θ)
Therefore,
csc²(300°) = 1 / sin²(300°)
In a unit circle, the sine of 300° is the same as the sine of -60° (since the sine function is periodic with a period of 360°). The sine of -60° is -√3/2. Plugging this into the cosecant squared formula gives us:
csc²(300°) = 1 / (-√3/2)² = 1 / (3/4) = 4/3
Thus, the exact value of csc²(300°) is 4/3.