Question

Find the coordinates of the point (a, b).

Answer 1

Answer:

a = $\frac{1}{\sqrt{2} }$ and b = $\frac{\sqrt{2} }{2}$

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 = $\frac{\sqrt{2} }{2}$

• Cos(45) = adjacent side / hypotenuse

<=> Cos(45) = a / 1

<=> a =  Cos(45)*1 = $\frac{1}{\sqrt{2} }$

So: a = $\frac{1}{\sqrt{2} }$ and b = $\frac{\sqrt{2} }{2}$