The table shows some values of x and y that satisfy the equation y = a cos(x²) + b | x | 0 | 30 | 60 | 90 | 120 | 150 | 180 | |------|-----|------|------|------|-------|-------|-------| | y | 3 | 1 + √3 | 2 | 1 | 0 | 1 - √3 | -1 | Find the value of y when x = 45. - Edexcel - GCSE Maths - Question 20 - 2017 - Paper 1

Using the values for x = 0 and x = 60, we can form two equations:

1. For x = 0:
   $y = a \cos(0^2) + b = 3 \implies a + b = 3$

2. For x = 60:
   $y = a \cos(60^2) + b = 2 \implies a \cos(3600) + b = 2$
   Since ( \cos(3600) = \cos(0) = 1 ), this simplifies to
   $a + b = 2$

We have the following system of equations:

1. $a + b = 3$
2. $a + b = 2$

However, the above equations are contradictory as they cannot simultaneously be true. A typical approach could involve assuming one variable and substituting, but since this situation leads to a contradiction, we need to identify the correct constants directly from the context or specification.

At x = 45 degrees, we can find y directly from the form of the equation if we had found a and b correctly. However, given the context of the table:

We will interpolate or use existing values, recognizing the pattern in x and y. For x = 45, consider the pattern: From x = 30 to x = 60, it appears that y values increase and decrease in a predictable, periodic function. Using known values, we estimate as follows:

If we interpolate between y values at x = 30 (1 + √3) and x = 60 (2), we expect y to be 1.5 at x = 45 as an approximation. Thus,

$y(45) \approx 1.5$.