Answer
$\dfrac{\sqrt 2}{2}$
Work Step by Step
The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant -II: $(\pi-\theta)$
c) Quadrant- III: $(\theta - \pi)$
d) Quadrant - IV: $(2\pi - \theta)$
First, we reduce the angle:
$495^{\circ}-360^{\circ}=135^{\circ}$
Since we are in quadrant 2, we subtract from $180^{\circ}$
$180^{\circ}-135^{\circ}=45^{\circ}$
Thus, we have $\sin 45^{\circ}=\dfrac{\sqrt 2}{2}$
The value is positive because sine is positive in the 2nd quadrant.
