Find the value of ( sin(330^circ) ) using the unit circle

Question

Accepted Answer

Step:1 ：First, we convert the angle from degrees to radians. Since (360^circ = 2pi ) radians, we can say that (330^circ = frac{330}{360} cdot 2pi = frac{11}{6}pi ) radians.Step:2 ：Next, we locate this angle on the unit circle. The angle (frac{11}{6}pi ) radians corresponds to the point ((sqrt{3}/2, -1/2)) on the unit circle. The y-coordinate of this point gives us the value of (sin(frac{11}{6}pi)).Step:3 ：Therefore, the value of ( sin(330^circ) = sin(frac{11}{6}pi) = -1/2 ).

Answer

Step: 1 ：First, we convert the angle from degrees to radians. Since (360^circ = 2pi ) radians, we can say that (330^circ = frac{330}{360} cdot 2pi = frac{11}{6}pi ) radians.Step: 2 ：Next, we locate this angle on the unit circle. The angle (frac{11}{6}pi ) radians corresponds to the point ((sqrt{3}/2, -1/2)) on the unit circle. The y-coordinate of this point gives us the value of (sin(frac{11}{6}pi)).Step: 3 ：Therefore, the value of ( sin(330^circ) = sin(frac{11}{6}pi) = -1/2 ).

Find the value of \( \sin(330^\circ) \) using the unit circle

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