A Dictionary of science, literature, and art [electronic resource]: comprising the history, description, and scientific principles of every branch of human knowledge; with the derivation and definition of all the terms in general use (1844)
Brande, William Thomas, 1788-1866, Cauvin, Joseph · New York : Harper & brothers · leaf 1278
Hi,and.A H3 = A Hi; therefore sirr(180° + A) =— sin A, andcos (180 + A) = — cos A. In the fourth quadrant we haveA 04 = 270° + A; the sine is C4 H4 negative, and the cosineis A H4 positive. But C4 H4>= A Hi, and A H4 = Ci Hi;therefore sin (270° + A) = — cos A, and cos (270° +A) =sin A. Having… … cos A sin A cosec A = cos A sin A Whence it appears that the tangent and cotangent will bepositive when the sine and cosine have both the same sign,that is, in fhe,first and third quadrants; and negative whenthe sine and cosine have opposite signs, that is, in the sec-ond and fourth quadrants. It…
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