Evaluate the following summation (make sure your calculator is in radian mode): 
${\sum }_{i=1}^4\sin \left(\frac{\pi i}{8}\right)$

• A. 1.00
• B. 1.38
• C. 3.01
• D. 0.62

Answer: (C)

Verified step by step guidance

1. Identify the summation expression: \( \sum_{i=1}^4 \sin\left(\frac{\pi i}{8}\right) \). This means you need to evaluate the sine function for each integer value of \( i \) from 1 to 4 and then sum the results.
2. Set your calculator to radian mode, as the angles in the sine function are given in radians. This is crucial for obtaining the correct values of the sine function.
3. Calculate \( \sin\left(\frac{\pi \times 1}{8}\right) \). This involves substituting \( i = 1 \) into the expression and evaluating the sine of the resulting angle.
4. Calculate \( \sin\left(\frac{\pi \times 2}{8}\right) \). Substitute \( i = 2 \) into the expression and evaluate the sine of the resulting angle.
5. Repeat the process for \( i = 3 \) and \( i = 4 \), calculating \( \sin\left(\frac{\pi \times 3}{8}\right) \) and \( \sin\left(\frac{\pi \times 4}{8}\right) \) respectively. Finally, sum all the calculated sine values to get the result of the summation.