What is the value of sin(112.5) ?

The value of sin(112.5) is (sqrt(2+\sqrt{2)})/2

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sin(112.5)

sin (112. 5^{\circ})

\frac{2 + 2}{2}

Solution steps

sin (112. 5^{\circ})

Rewrite using trig identities:

sin (67. 5^{\circ})

= sin (67. 5^{\circ})

Rewrite using trig identities:

\frac{1 - cos ( 13 5 ^{\circ} )}{2}

= \frac{1 - cos ( 13 5 ^{\circ} )}{2}

Use the following trivial identity:

cos (13 5^{\circ}) = - \frac{2}{2}

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

Simplify

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

= \frac{2 + 2}{2}

sin (8)

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

sec (24 0^{\circ})

tan (- \frac{5 π}{12})

tan (1 0^{\circ})

What is the value of sin(112.5) ?
The value of sin(112.5) is (sqrt(2+\sqrt{2)})/2