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12.3 Caleulate the value of \( \cot 65^{\circ} \) correct to TWO decimal places. \( \frac{63}{100} \) \( =0.66 \)

Ask by Long Christensen. in South Africa
Feb 19,2025

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The value of \( \cot 65^{\circ} \) is approximately -0.68.

Solution

Calculate or simplify the expression \( \cot(65) \). Calculate the value by following steps: - step0: Calculate: \(\cot\left(65\right)\) The value of \( \cot 65^{\circ} \) is approximately -0.680254. Therefore, the value of \( \cot 65^{\circ} \) correct to TWO decimal places is -0.68.

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Did you know that the cotangent function is the reciprocal of the tangent? This means that if you want to find \( \cot 65^{\circ} \), you could simply calculate \( \frac{1}{\tan 65^{\circ}} \). With a scientific calculator, you would find that \( \tan 65^{\circ} \) is approximately 2.1445. Thus, \( \cot 65^{\circ} \) comes out to about \( 0.466 \), which rounds to 0.47! When tackling trigonometric calculations, a common mistake is forgetting to switch your calculator from degrees to radians or vice versa! Make sure you're in the right mode before performing your calculations, as this can lead to significant errors in your results. Also, double-check your final rounding to ensure you're aligning it with the required decimal places!

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