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Sum and difference identities

Find the coordinates of P(π/12)

x = (1+√3)/(2√2)

To find the y-coordinate you use the identity:
sin(α - β) = (sinα)(cosβ) (cosα)(sinβ)

Why do we use this identity? eg, why don't we use
sin(α + β) = (sinα)(cosβ) + (cosα)(sinβ) ??

Solution Preview

To find y_coordinate, we can use
y=sqrt(1-x^2)=(-1+√3)/(2√2)

If we use identities, then we let β=π/12 and α=π/6, then ...

Solution Summary

This shows how to use the difference identity to find coordinates.

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