What is the value of sec(45°)? (2019)

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Question: What is the value of sec(45°)? (2019)

Options:

Correct Answer: √2

Exam Year: 2019

Solution:

sec(45°) = 1/cos(45°) = 1/(√2/2) = √2.

What is the value of sec(45°)? (2019)

What is the value of sec(45°)? (2019)

Step 1: Understand that sec(θ) is the secant function, which is the reciprocal of the cosine function.
Step 2: Write the formula for secant: sec(θ) = 1/cos(θ).
Step 3: Substitute 45° into the formula: sec(45°) = 1/cos(45°).
Step 4: Find the value of cos(45°). The value of cos(45°) is √2/2.
Step 5: Substitute the value of cos(45°) into the equation: sec(45°) = 1/(√2/2).
Step 6: Simplify the expression: 1/(√2/2) is the same as 1 * (2/√2) = 2/√2.
Step 7: To simplify 2/√2, multiply the numerator and denominator by √2: (2√2)/(√2 * √2) = 2√2/2 = √2.

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