Find the Value Using the Unit Circle sec(30)

Problem

sec(30)

Solution

1. Identify the relationship between the secant function and the cosine function using the reciprocal identity.

sec(30)=1/cos(30)

2. Determine the value of cos(30) using the unit circle or a standard 30−60−90 reference triangle.

cos(30)=√(,3)/2

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

sec(30)=1/√(,3)/2

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

sec(30)=2/√(,3)

5. Rationalize the denominator by multiplying the numerator and the denominator by √(,3)

sec(30)=(2√(,3))/3

Final Answer

sec(30)=(2√(,3))/3

Want more problems? Check here!