Answer:
a = [tex]\frac{1}{\sqrt{2} }[/tex] and b = [tex]\frac{\sqrt{2} }{2}[/tex]
Step-by-step explanation:
As we know, the radius of the unit circle is 1 unit (it is the hypotenuse in the right triangle, the blue line)
We use trigonometric formulas to find out a and b
- Sin(45) = opposite side / hypotenuse
<=> Sin(45) = b / 1
<=> b= Sin(45)*1 = [tex]\frac{\sqrt{2} }{2}[/tex]
- Cos(45) = adjacent side / hypotenuse
<=> Cos(45) = a / 1
<=> a = Cos(45)*1 = [tex]\frac{1}{\sqrt{2} }[/tex]
So: a = [tex]\frac{1}{\sqrt{2} }[/tex] and b = [tex]\frac{\sqrt{2} }{2}[/tex]
