Based on all the information given by the statement, the exact value of the sine function of angle A is √5 / 3.
According to the statement presented in this question we know the exact value of the cosine function of an angle and the fact that such angle is in the first quadrant of a Cartesian plane. In this case, both the sine and the cosine of the angle are positive quantities and both functions are related by the fundamental trigonometric formula:
sin θ = √[1 - cos² θ]
sin θ = √[1 - (2 / 3)²]
sin θ = √5 / 3
Based on all the information given by the statement, the exact value of the sine function of angle A is √5 / 3.
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