Answer:
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
