Find the Value Using the Unit Circle csc(45)

Problem

csc(45)

Solution

1. Identify the relationship between the cosecant function and the sine function using the reciprocal identity.

csc(45)=1/sin(45)

2. Determine the value of sin(45) using the unit circle or a special right triangle (45−45−90.

sin(45)=√(,2)/2

3. Substitute the sine value back into the reciprocal identity.

csc(45)=1/√(,2)/2

4. Simplify the complex fraction by multiplying by the reciprocal of the denominator.

csc(45)=2/√(,2)

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

csc(45)=(2√(,2))/2

6. Reduce the fraction to its simplest form.

csc(45)=√(,2)

Final Answer

csc(45)=√(,2)

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