Question

find the coordinates of the point $(a,b)$.
a =?
○ 1
○ $sqrt{2}$
○ $\frac{sqrt{2}}{2}$
done

b =?
○ 1
○ $sqrt{2}$
○ $\frac{sqrt{2}}{2}$
done

Explanation:

Step1: Recall the unit - circle coordinates formula

For a point \((a,b)\) on the unit circle \(x^{2}+y^{2}=1\), if the angle \(\theta\) is made with the positive \(x\) - axis, then \(a = \cos\theta\) and \(b=\sin\theta\). Here \(\theta = 45^{\circ}=\frac{\pi}{4}\) radians.

Step2: Calculate the value of \(a\)

We know that \(\cos\frac{\pi}{4}=\frac{\sqrt{2}}{2}\).

Step3: Calculate the value of \(b\)

We know that \(\sin\frac{\pi}{4}=\frac{\sqrt{2}}{2}\).

Answer:

For \(a\): \(\frac{\sqrt{2}}{2}\)
For \(b\): \(\frac{\sqrt{2}}{2}\)