Question

Please help !!!! Find the exact value of sin 120°.

Answer 1

Sin of 120 degrees, on a unit circle, would have coordinates of (-1/2, √3/2). Since the sin is the y coordinate, the answer is √3/2, or C.

Answer 2

Answer:

$sin120^{\circ}= \frac{\sqrt{3}}{2}$

Option (C) is correct.

Step-by-step explanation:

By using the trigonometric identity

$sin\theta = cos (90^{\circ}- \theta)$

As given in the question.

$\theta = 120^{\circ}$

Put in the above

$sin120^{\circ} = cos (90^{\circ}- 120^{\circ})$

$sin120^{\circ} = cos(-30^{\circ})$

$As\ cosine\ is\ an\ even\ function\ i.e\ cos (-\theta) = cos (\theta).$

i.e

$cos30^{\circ} = cos(-30^{\circ})$

$use\ the\ above\ result\ in\ sin120^{\circ} = cos(-30^{\circ})$

Thus

$sin120^{\circ} = cos(30^{\circ})$

As

$cos30^{\circ}= \frac{\sqrt{3}}{2}$

Therefore

$sin120^{\circ}= \frac{\sqrt{3}}{2}$

Option (C) is correct.