What is the value of sin(5/8 pi) ?

The value of sin(5/8 pi) is (sqrt(2+\sqrt{2)})/2

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sin(5/8 pi)

sin (\frac{5}{8} π)

\frac{2 + 2}{2}

Solution steps

sin (\frac{5}{8} π)

Simplify:

\frac{5}{8} π = \frac{5 π}{8}

= sin (\frac{5 π}{8})

Rewrite using trig identities:

sin (\frac{3 π}{8})

= sin (\frac{3 π}{8})

Rewrite using trig identities:

\frac{1 - cos ( \frac{3 π}{4} )}{2}

= \frac{1 - cos ( \frac{3 π}{4} )}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

= \frac{1 - ( - \frac{2}{2} )}{2}

Simplify

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

= \frac{2 + 2}{2}

(- 1) - arctan (- 1)

cos (30 π)

8 \cdot sin (2 4^{\circ})

ln ∣ 4 + tan (0) ∣

ln ∣ sec (0) + tan (0) ∣

What is the value of sin(5/8 pi) ?
The value of sin(5/8 pi) is (sqrt(2+\sqrt{2)})/2