What is the value of cos((3pi)/(16)) ?

The value of cos((3pi)/(16)) is (sqrt(2+\sqrt{2-\sqrt{2)}})/2

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cos((3pi)/(16))

cos (\frac{3 π}{16})

\frac{2 + 2 - 2}{2}

Solution steps

cos (\frac{3 π}{16})

Rewrite using trig identities:

\frac{1 + cos ( \frac{3 π}{8} )}{2}

= \frac{1 + cos ( \frac{3 π}{8} )}{2}

Rewrite using trig identities:

cos (\frac{3 π}{8}) = \frac{2 - 2}{2}

= \frac{1 + \frac{2 - 2}{2}}{2}

Simplify

\frac{1 + \frac{2 - 2}{2}}{2} : \frac{2 + 2 - 2}{2}

= \frac{2 + 2 - 2}{2}

2 cos (\frac{π}{2}) + sin (2 \cdot \frac{π}{2})

4 + 4 cos (\frac{π}{2})

20 \cdot sin (12 0^{\circ})

sin (61.9 3^{\circ})

3 sec (\frac{π}{4}) tan (\frac{π}{4}) + 10 csc^{2} (\frac{π}{4})

What is the value of cos((3pi)/(16)) ?
The value of cos((3pi)/(16)) is (sqrt(2+\sqrt{2-\sqrt{2)}})/2