The table shows some values of x and y that satisfy the equation y = a cos x° + b | x | 0 | 30 | 60 | 90 | 120 | 150 | 180 | |----|----|----|----|----|-----|-----|-----| | y | 3 | 1 + \sqrt{3} | 2 | 1 | 0 | 1 - \sqrt{3} | -1 | Find the value of y when x = 45 - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 1

Based on the generating function provided, we substitute x = 45 into the equation:

$y = a \cos(45°) + b$

From the table, we need to find a and b by using the known points in the table.

Let's select two points, for example, when x = 0 and x = 90.

1. When x = 0: $y = a \cos(0°) + b \rightarrow 3 = a + b$

2. When x = 90: $y = a \cos(90°) + b \rightarrow 1 = 0 + b \rightarrow b = 1$

Substituting b = 1 in the first equation:

$3 = a + 1 \rightarrow a = 2$

Now we can substitute a and b into the original function:

$y = 2 \cdot \frac{\sqrt{2}}{2} + 1 \rightarrow y = \sqrt{2} + 1$

Thus, the value of y when x = 45 is:

Final Result:

$y = \sqrt{2} + 1$