The table shows some values of x and y that satisfy the equation y=acosx + b

By an online search, i found that the table is:

x = 0°       30°         60°    90°    120°      150°       180°

y= 10     4+3*√3        7       4       1        4 -3*√3      -2

Where x is in degrees.

And we want to find the value of y, when x = 45°.

And our equation is:

y = a*cos(x) + b

Notice that we have two variables in our equation, a and b, then we need to choose two of the points in the table to write equations.

I will choose te points

x = 0°, y = 10

and

x = 90°, y = 4

Now we can replace these values in the equatio to get:

10 = a*cos(0°) + b

4 = a*cos(90°) + b

We know that:

cos(0°) = 1

cos(90°) = 0

(because of those relationships is that i choosen these points)

Replacing that in the equations, we get:

10 = a*1 + b = a + b

4 = a*0 + b = b

From the second equation, we get:

b = 4

Now we can replace this in the first equation to get:

10 = a + b = a + 4

10 - 4 = a = 6

Then our equation is:

y = 6*cos(x) + 4.

Now we want to find the value of y when x = 45, to do it, we just replace the value of x in that equation:

y = 6*cos(45°) + 4 = 6*(√2/2) + 4 = 8.24

answer: 1 and 3

step-by-step explanation: