Simplify csc(270)

Problem

csc(270)

Solution

1. Identify the definition of the cosecant function in terms of the sine function.

csc(θ)=1/sin(θ)

2. Substitute the given angle into the identity.

csc(270)=1/sin(270)

3. Evaluate the sine of 270 using the unit circle, where the coordinates at 270 are (0,−1)

sin(270)=−1

4. Simplify the fraction by dividing the numerator by the denominator.

1/(−1)=−1

Final Answer

csc(270)=−1

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