Question

find the exact value by using half - angle identity
sing pi/8
Help plzz

Answer 1

\(\bf sin\left(\cfrac{\pi}{8}\right)\\ \quad \\ \quad \\
2\times \cfrac{1}{8}\implies \cfrac{1}{4}\qquad thus\\ \quad \\
sin\left(\cfrac{\pi}{8}\right)\implies sin\left(\cfrac{\frac{\pi}{4}}{2}\right)\)

use that in your half-angle trig identity for sine

Answer 2

\[\sin \pi/4/2= -+\sqrt{1-cosx}/2\]

Answer 3

yeap

Answer 4

i cant finish it

Answer 5

.. why not?

Answer 6

what i have to used for cos x

Answer 7

\(\bf sin\left(\cfrac{\frac{\pi}{4}}{2}\right)=\sqrt{\cfrac{1-cos\left(\frac{\pi}{4}\right)}{2}}\)


that angle will be in the Unit Circle

Answer 8

\[-+\sqrt{1-\sqrt{2}/2 }/2\]

Answer 9

ahemm so... \(\bf sin\left(\cfrac{\frac{\pi}{4}}{2}\right)=\sqrt{\cfrac{1-\frac{\sqrt{2}}{2}}{2}}\implies \sqrt{\cfrac{\frac{2-\sqrt{2}}{2}}{2}}\implies \sqrt{\cfrac{2-\sqrt{2}}{2}\cdot \cfrac{1}{2}}\)

Answer 10

\[\sqrt{2-\sqrt{2}/}4 \]

Answer 11

yeap, can't simplify it further