Given sin⁡300°, determine its equivalent expression.

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yunitsiL · Accepted Answer

One full rotation on the unit circle is $360^{\circ}$ so $300^{\circ} - 360^{\circ} = - 60^{\circ}$ is a coterminal angle to $300^{\circ} 3$ . One possible equivalent expression could then be $\sin 300^{\circ} = \sin (- 60^{\circ})$ .
Since sine is an odd function, then $\sin (- θ) = - \sin θ . Therefore \sin (- 60^{\circ}) = - \sin 60^{\circ}$ $A second possible equivalent expression could then be \sin 300^{\circ} = - \sin 60^{\circ}$

Sine is symmetric to the y-axis.

Since $300^{\circ}$ is $30^{\circ}$ to the right of the negative y-axis and $240^{\circ}$ is $30^{\circ}$ to the left of the negative y-axis, then $300^{\circ}$ and $240^{\circ}$ must have the same value for sine. A third possible expression could then be $\sin 300^{\circ}$ = $\sin 240^{\circ} .$
If we evaluate sin300∘, we need to look at the y-coordinate of the point at $300^{\circ}$ on the unit circle.

The point at $300^{\circ}$ is $(\frac{1}{2}, - (\sqrt{\frac{3}{2}})$ so a fourth possible equivalent expression could be $\sin 300^{\circ} = - (\sqrt{\frac{3}{2}}) .$

Given sin300°, determine its equivalent expression.

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