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\(\mathsf{sin\!\left(\dfrac{3\pi}{4}\right)}\\\\\\ =\mathsf{sin\!\left(\dfrac{3\cdot 180^\circ}{4}\right)}\\\\\\ =\mathsf{sin(135^\circ)}\\\\ =\mathsf{sin(180^\circ-135^\circ)}\)
\(=\mathsf{sin(45^\circ)}\\\\ =\mathsf{\dfrac{\sqrt{2}}{2}}\quad\longleftarrow\quad\textsf{this is the answer.}\)
I hope this helps.=)
Tags: sine sin common angles trig trigonometry
