HP 40gs hp 40gs_user's guide_English_E_HDPMSG40E07A.pdf - Page 222

hp40g+.book Page 40 Friday, December 9, 2005 1:03 AM HALFTAN SINCOS TAN2CS2 14-40 Typing: ATAN2S(ATAN(X)) gives: asin ⎛ ⎜ ---------x ⎝ x2 + 1⎠ Transform in terms of tan(x/2) HALFTAN has a trigonometric expression as an argument. HALFTAN transforms sin(x), cos(x) and tan(x) in the expression, rewriting them in terms of tan(x/2). Typing: HALFTAN(SIN(X)2 + COS(X)2) gives (SQ(X) = X2): ⎛ ⎜ 2 ⋅ tan ⎛ ⎝ 2-x-⎠⎞ ⎞2 ⎟ ⎛ ⎜ 1 - S Q ⎛ ⎝ tan ⎛ ⎝ 2-x-⎠⎞ ⎞ ⎠ ⎞ ⎟ 2 ⎜ ⎝ SQ⎝⎛ tan ⎝⎛ 2-x + 1⎠⎟ ⎜ ⎝ SQ⎝⎛ tan ⎛ ⎝ 2-x-⎠⎞ ⎞ ⎠ + 1⎠⎟ or, after simplification: 1 Transform the complex exponentials into sin and cos SINCOS takes an expression containing complex exponentials as an argument. SINCOS then rewrites this expression in terms of sin(x) and cos(x). Typing: SINCOS(EXP(i · X)) gives after turning on complex mode, if necessary: cos(x) + i · sin(x) Transform tan(x) with sin(2x) and cos(2x) TAN2CS2 has a trigonometric expression as an argument. Computer Algebra System (CAS)