What is the value of sin(2arccos(-(sqrt(2))/2)) ?

The value of sin(2arccos(-(sqrt(2))/2)) is -1

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sin(2arccos(-(sqrt(2))/2))

sin (2 arccos (- \frac{2}{2}))

- 1

Solution steps

sin (2 arccos (- \frac{2}{2}))

Rewrite using trig identities:

2 sin (arccos (- \frac{2}{2})) cos (arccos (- \frac{2}{2}))

= 2 sin (arccos (- \frac{2}{2})) cos (arccos (- \frac{2}{2}))

Rewrite using trig identities:

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

Rewrite using trig identities:

cos (arccos (- \frac{2}{2})) = - \frac{2}{2}

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

Simplify

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

= - 1

sin (\frac{3}{8})

sin (\frac{\frac{2 π}{3}}{2})

arcsin (\frac{9}{14})

sin (\frac{15 π}{8})

5 sin (17 0^{\circ})

What is the value of sin(2arccos(-(sqrt(2))/2)) ?
The value of sin(2arccos(-(sqrt(2))/2)) is -1