Question

The approximate value of \( \sec 59^\circ \) obtained by taking \( 1^\circ = 0.0174 \) and \( \sqrt{3} = 1.732 \) is:

• A. \( 1.9849 \)
• B. \( 1.8493 \)
• C. \( 1.9397 \)
• D. \( 1.9948 \) \bigskip

Hint:

For trigonometric approximations, always use the correct unit conversion and identity. The secant function is the reciprocal of cosine, and knowing the conversion from degrees to radians is essential.

Answer 1

The Correct Option is C

We are given that \( 1^\circ = 0.0174 \), so to convert degrees to radians, we calculate: \[ 59^\circ = 59 \times 0.0174 = 1.0266. \] Now, using the formula for secant, \( \sec \theta = \frac{1}{\cos \theta} \), we find: \[ \sec 59^\circ \approx 1.9397. \] Thus, the correct answer is \( 1.9397 \). \bigskip