Discuss the continuity of the cosine, cosecant, secant and cotangent functions,

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These are called co-functions. For example sine 43 is equal to cosine 47. for every right triangle, it is equal to 90 degrees. that is why sine 43 and cosine 47 is equal because 43+47 = 90. same goes for tangent - cotangent, secant - cosecant and etc ...