Question

Find the exact value of sin (1) ОА. (2 + 2 OB. - /2- & y 2 2+ OC O C.-12+a 2 O D. V2-√2 O 2

Answer 1

Okay, here we have this:

Considering the provided sin, we are going to calculate it, so we obtain the following:

`\begin{gathered} \sin \mleft((7\pi)/(8)\mright) \\ =\cos \mleft((\pi)/(2)-(7\pi)/(8)\mright) \\ =\cos \mleft(-(3\pi)/(8)\mright) \\ =\cos \mleft((3\pi)/(8)\mright) \\ =\cos \mleft(((3\pi)/(4))/(2)\mright) \\ =\sqrt{(1+\cos\left((3\pi)/(4)\right))/(2)} \\ =\sqrt{(1+\left(-(√(2))/(2)\right))/(2)} \\ =\sqrt{(2-√(2))/(4)} \\ =\frac{\sqrt{2-√(2)}}{2} \end{gathered}`

Finally we obtain that the correct answer is the option D.