Evaluate csc(45 degrees )

Problem

csc(45)

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 of 45 into the identity.

csc(45)=1/sin(45)

3. Recall the exact value of sin(45) from the unit circle or a special right triangle.

sin(45)=√(,2)/2

4. Simplify the expression by taking the reciprocal of the sine value.

csc(45)=1/√(,2)/2

5. Rationalize the denominator by multiplying the numerator and denominator by √(,2)

csc(45)=2/√(,2)

csc(45)=√(,2)

Final Answer

csc(45)=√(,2)

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