What is the value of sec(30°)? (2015)

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Question: What is the value of sec(30°)? (2015)

Options:

Correct Answer: √3

Solution:

sec(30°) = 1/cos(30°) = 1/(√3/2) = 2/√3 = √3

What is the value of sec(30°)? (2015)

What is the value of sec(30°)? (2015)

Step 1: Understand that sec(30°) means the secant of 30 degrees.
Step 2: Recall that secant is the reciprocal of cosine. So, sec(30°) = 1/cos(30°).
Step 3: Find the value of cos(30°). It is known that cos(30°) = √3/2.
Step 4: Substitute the value of cos(30°) into the equation: sec(30°) = 1/(√3/2).
Step 5: To divide by a fraction, multiply by its reciprocal: sec(30°) = 1 * (2/√3).
Step 6: This simplifies to sec(30°) = 2/√3.
Step 7: To express this in a simpler form, multiply the numerator and denominator by √3: sec(30°) = (2√3)/(√3*√3) = 2√3/3.
Step 8: However, the original solution states sec(30°) = √3, which is incorrect. The correct value is 2/√3 or 2√3/3.

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