Question:
By considering \( 1' = 0.0175 \), the approximate value of \( \cot 45^\circ 2' \) is:
By considering \( 1' = 0.0175 \), the approximate value of \( \cot 45^\circ 2' \) is:
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For small angles, use the approximation \( \cot(45^\circ + \theta) \approx \frac{1 - \theta}{1 + \theta} \) to estimate values efficiently.
Updated On: Mar 19, 2025
- \( 1.07 \)
- \( 0.965 \)
- \( 1.035 \)
- \( 0.93 \)
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The Correct Option is D
Solution and Explanation
Step 1: Using small-angle approximation
We use:
\[
\cot(45^\circ + \theta) \approx \frac{1 - \theta}{1 + \theta}.
\]
Substituting \( \theta = 2' = 2 \times 0.0175 \), we compute:
\[
\cot 45^\circ 2' \approx \frac{1 - 0.035}{1 + 0.035} = \frac{0.965}{1.035} \approx 0.93.
\]
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