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Find the exact value of the trigonometric function at the given real number. csc 11π3

User Wildfire
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Final answer:

To find csc(11π/3), we need to find the value of sin(11π/3) and then take its reciprocal. In the third quadrant, sin(11π/3) is -(√3/2). Therefore, csc(11π/3) = -2√3/3.

Step-by-step explanation:

The trigonometric function that you are asked to find is the cosecant function of 11π/3.

The cosecant function is the reciprocal of the sine function. So, to find csc(11π/3), we need to find the value of sin(11π/3) and then take its reciprocal.

First, let's find sin(11π/3). In 11π/3, the angle is in the third quadrant where sine is negative. So, we can apply the reference angle of π/3 to find the exact value.

The reference angle of π/3 is π/3 - π = 2π/3.

Since sin(2π/3) = √3/2, and sin is negative in the third quadrant, sin(11π/3) = -(√3/2).

Taking the reciprocal, csc(11π/3) = -2/√3 = -2√3/3.

User Kondal
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