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In the previous lesson, we saw that (cosθ,sinθ) are the coordinates of a point on the unit circle whose angle to the x-axis is θ:
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If we trace the values of sinθ and cosθ with θ on the x-axis, we find their sinusoidal graphs:
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Looking at them more closely:
Sine and Cosine functions
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Notice that both sinx and cosx have a domain of x∈R and a range of (−1,1).
The range is a consequence of the fact that these values come from coordinates on a unit circle, which are always between −1 and 1.
Notice also that cosx "lags" behind sinx by 2π. Mathematically we can write
Sinusoidal Functions
A sinusoidal function is a generalization of sin and cos to the form
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or
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These functions are very useful for modeling periodic phenomena, such as tides or circular motion.
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