Question

Using the figure, establish the value of the function y=sinθ when θ=π3 . (1 point) Responses 12 Start Fraction 1 over 2 End Fraction 2√2 Start Fraction Start Root 2 End Root over 2 End Fraction 3√2 Start Fraction Start Root 3 End Root over 2 End Fraction 12√ Start Fraction 1 over Start Root 2 End Root End Fraction

Answer 1

To find the value of the function \( y = \sin \theta \) when \( \theta = \frac{\pi}{3} \):

1. Recall that \( \sin \theta \) represents the y-coordinate of a point on the unit circle corresponding to the angle \( \theta \).
2. The angle \( \frac{\pi}{3} \) radians is equivalent to \( 60^\circ \).
3. The sine of \( 60^\circ \) (or \( \frac{\pi}{3} \)) is a well-known trigonometric value.

\[ \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \]

Thus, the value of \( y = \sin \theta \) when \( \theta = \frac{\pi}{3} \) is:

\[ \frac{\sqrt{3}}{2} \]

Therefore, the correct response is:

\[ 3\sqrt{2} \cdot \frac{\sqrt{3}}{2} \]

However, based on the fraction provided, the answer is:

\[ \frac{\sqrt{3}}{2} \]