Using the figure, establish the value of the function y=sinθ when θ=π3 .

Question

(1 point)
Responses

3√2
Start Fraction Start Root 3 End Root over 2 End Fraction

12
Start Fraction 1 over 2 End Fraction

2√2
Start Fraction Start Root 2 End Root over 2 End Fraction

12√
Start Fraction 1 over Start Root 2 End Root End Fraction
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Answer 1

To find the value of the function \( y = \sin \theta \) when \( \theta = \frac{\pi}{3} \), we can reference the sine values of common angles.

The sine of \( \frac{\pi}{3} \) (or 60 degrees) is known to be:

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

Thus, the response that corresponds to this is:

Start Fraction Start Root 3 End Root over 2 End Fraction

So, the value of \( y = \sin\left(\frac{\pi}{3}\right) \) is \( \frac{\sqrt{3}}{2} \).