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Find the exact value of the sine function of the given angle. 2220° sin 2220°=

User SeeTheC
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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:

User BazZy
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