Answer:
[tex]sin120^{\circ}= \frac{\sqrt{3}}{2}[/tex]
Option (C) is correct.
Step-by-step explanation:
By using the trigonometric identity
[tex]sin\theta = cos (90^{\circ}- \theta)[/tex]
As given in the question.
[tex]\theta = 120^{\circ}[/tex]
Put in the above
[tex]sin120^{\circ} = cos (90^{\circ}- 120^{\circ})[/tex]
[tex]sin120^{\circ} = cos(-30^{\circ})[/tex]
[tex]As\ cosine\ is\ an\ even\ function\ i.e\ cos (-\theta) = cos (\theta).[/tex]
i.e
[tex]cos30^{\circ} = cos(-30^{\circ})[/tex]
[tex]use\ the\ above\ result\ in\ sin120^{\circ} = cos(-30^{\circ})[/tex]
Thus
[tex]sin120^{\circ} = cos(30^{\circ})[/tex]
As
[tex]cos30^{\circ}= \frac{\sqrt{3}}{2}[/tex]
Therefore
[tex]sin120^{\circ}= \frac{\sqrt{3}}{2}[/tex]
Option (C) is correct.
