Use identities to correctly complete each sentence.

If sin θ = ⅔, then -sin(-θ) = ________________.

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Recall the identity for the sine of a negative angle: \(\sin(-\theta) = -\sin(\theta)\).

Apply this identity to rewrite \(-\sin(-\theta)\) as \(-(-\sin(\theta))\).

Simplify the expression: \(-(-\sin(\theta)) = \sin(\theta)\).

Since it is given that \(\sin(\theta) = \frac{2}{3}\), substitute this value into the expression.

Therefore, \(-\sin(-\theta) = \frac{2}{3}\).

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The sine function relates an angle in a right triangle to the ratio of the opposite side over the hypotenuse. It is defined for all real numbers and can take values between -1 and 1. Knowing the sine value of an angle helps determine related trigonometric expressions.

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Sine is an odd function, meaning sin(-θ) = -sin(θ). This property allows us to simplify expressions involving negative angles by changing the sign of the sine value, which is crucial for evaluating expressions like -sin(-θ).

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