Given:
On a unit circle, the terminal point of θ is [tex]\left(\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)[/tex].
To find:
The value of [tex]\theta[/tex].
Solution:
If the terminal point of θ is (x,y), then
[tex]\tan \theta=\dfrac{y}{x}[/tex]
On a unit circle, the terminal point of θ is [tex]\left(\dfrac{\sqrt{2}}{2},\dfrac{\sqrt{2}}{2}\right)[/tex]. So,
[tex]\tan \theta=\dfrac{\dfrac{\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}[/tex]
[tex]\tan \theta=1[/tex]
[tex]\tan \theta=\tan \dfrac{\pi}{4}[/tex]
[tex]\theta=\dfrac{\pi}{4}[/tex]
Therefore, the correct option is D.
