What is the value of sin(2((3pi)/4)) ?

The value of sin(2((3pi)/4)) is -1

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sin(2((3pi)/4))

sin (2 (\frac{3 π}{4}))

- 1

Solution steps

sin (2 (\frac{3 π}{4}))

= sin (2 \cdot \frac{3 π}{4})

Rewrite using trig identities:

2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

= 2 sin (\frac{3 π}{4}) cos (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

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

Simplify

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

= - 1

tan (22. 4^{\circ})

cot (arccos (\frac{2}{2}))

arccos (- 0.998482)

cos (2) (1)

cos (2 \cdot (- 1625)) + 2 (- 1625)^{2} - 4