Putting a question mark at the end of a phrase does not make it a sensible of even an answerable question.
Sine and cosine of real numbers? Yes, they do exist. In fact, sines and cosines of complex numbers also exist. Does that answer the question?
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The domain of cosine is all real numbers, its range is [-1,1], and its period is 2π radians.
The negative sine graph and the positive sine graph have opposite signs: when one is negative, the other is positive - by exactly the same amount. The sine function is said to be an odd function. The two graphs for cosine are the same. The cosine function is said to be even.
Cosine (0) = 1 Sin(0) = 0 The sine and cosine curves are two intertwining curves, that complement each other, hence the words 'Sine (Curve) and Cosine ( COmplementary Curve).
half range cosine series or sine series is noting but it consderingonly cosine or sine terms in the genralexpansion of fourierseriesfor examplehalf range cosine seriesf(x)=a1/2+sigma n=0to1 an cosnxwhere an=2/c *integral under limits f(x)cosnxand sine series is vice versa
Cotangent is 1 / tangent. Since tangent is sine / cosine, cotangent is cosine / sine.