Question

Find the value of Sin1680°​

Answer 1

Answer:

−0.86602540378443864676372317075293618347140262690519

Answer 2

$\mathbf{\sin 1680^{\circ}=-\frac{\sqrt{3}}{2}}$

Step-by-step explanation:

• Given data

        Let

        X = Sin 1680°​    ...1)

• We know that

        Sin (n×360°+Ф)  = Sin Ф

        and

        Sin (n×360°-Ф)  = -Sin Ф

• Equation 1) can be written as

       X = Sin (5×360° -120°)

       X = - Sin 120°      ...2)

• We also know that

       Sin (90°+Ф)  = Cos Ф

• Equation 2) can be written as

        X = - Sin (90° +30°)

        X = - Cos 30°

        So

        $\mathbf{X=-\frac{\sqrt{3}}{2}}$

• $\mathbf{Means\ \sin 1680^{\circ}=-\frac{\sqrt{3}}{2}}$