Let x= sin(t) and y= cos(t). Then \(\displaystyle x^2+ y^2= sin^2(t)+ cos^2(t)= 1\) which has the unit circle as graph. You are also given that sin(t)= cos(t) so x= y. The graph of that is a straight line. (In fact, it is a diameter of the circle.) Both are satisfied where the straight line y= x crosses the circle \(\displaystyle x^2+ y^2= 1\). That is, \(\displaystyle x^2+ x^2= 2x^2= 1\) so \(\displaystyle x= \frac{1}{\sqrt{2}}= \frac{\sqrt{2}}{2}\). One solution is, as you give, \(\displaystyle t= \frac{\pi}{4}\). The other is half way around the circle, \(\displaystyle \frac{\pi}{4}+ \pi= \frac{5\pi}{4}\)