Answer: We can start by converting the given angle to an equivalent angle between 0° and 360°.
2220° = 6(360°) + 300°
So, we can say that:
sin 2220° = sin (6(360°) + 300°)
Using the identity sin (θ + 2πk) = sin θ, we can write:
sin (6(360°) + 300°) = sin 300°
Now we need to find the exact value of sin 300°.
Using the identity sin (180° - θ) = sin θ, we can write:
sin 300° = sin (180° + 120°)
Using the identity sin (180° + θ) = -sin θ, we can write:
sin (180° + 120°) = - sin 120°
We know that the exact value of sin 120° is √3/2 (we can use the 30°-60°-90° triangle).
Therefore, we can say that:
sin 2220° = sin (6(360°) + 300°) = sin 300° = - sin 120° = - √3/2
So, the exact value of the sine function of the angle 2220° is - √3/2.
Explanation: