Master Even/Odd Identities Of Sine – Simplify Trigonometric Expressions And Prove Identities With Ease

Even/Odd Identities (sine)

sin(-θ) = -sinθ

The even/odd identities for sine (sin) are as follows:

Even Identity:

sin(-x) = -sin(x)

This identity states that if we take the negative of an angle, the sine function of that negative angle is equal to the negative of the sine function of the original angle. In other words, the sine function is an even function, meaning that it is symmetric about the y-axis. For example, if sin(30°) = 0.5, then sin(-30°) = -0.5.

Odd Identity:

sin(x + π) = -sin(x)

This identity states that if we add π (pi radians) to an angle x, the sine function of the resulting angle is equal to the negative of the sine function of the original angle. In other words, the sine function is an odd function, meaning that it is symmetric about the origin. For example, if sin(45°) = 0.71, then sin(45° + π) = -0.71.

These identities are useful in simplifying trigonometric expressions and in proving trigonometric identities.

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