Answer:
y = [tex]3\sqrt{2} +4[/tex] ≈ 8.24
Step-by-step explanation:
Let's put some values of x and y into the equation to solve for a and b. We'll go with (60, 7) and (90, 4).
(60, 7): 7 = a * [tex]cos(60)[/tex] + b ---- by basic trig, cos(60) = 1/2, so:
7 = 0.5a + b
(90, 4): 4 = a * cos(90) + b ---- by basic trig, cos(90) = 0, so:
4 = b
We know b, so we can solve for a:
7 = 0.5a + 4
a = 6
Now, we have: y = 6cos(x) + 4
We can put 45 in for x and solve for y:
y = 6cos(45) + 4 ---- by basic trig, cos(45) = [tex]\sqrt{2} /2[/tex]
y = [tex]6*\frac{\sqrt{2} }{2} +4=3\sqrt{2} +4[/tex]
Thus, y = [tex]3\sqrt{2} +4[/tex] ≈ 8.24.
Hope this helps!
