Schaum's Outline of Theory and Problems of Beginning Calculus

CHAP. 281 THE TANGENT AND OTHER TRIGONOMETRIC FUNCTIONS 2199 7 t'Fig. 28-5Fig. 28-6Since tan (a2 - al) = 1,IIa2 - al = - radians = 45"4In general, given tan (a2 - al), the value of a2 - al can be estimated from the table in Appendix D.It should be noted that, in certain cases, the above method will yield the larger angle of intersection.Supplementary Problems28.8 Sketch the graphs of: (a) sec x; (b) cot x.tan U + tan U28.9 Prove the identity tan (U + U ) =1 - tan U tan U'28.11 Find y' by implicit differentiation:(4 tan (XY) = Y (b) sec' y + csc2 x = 3(c) tan2 (y + 1) = 3 sin x (4 y = tan2 (x + y)28.12 Find an equation of the tangent line to the curve y = tan x at the point (43, fi).28.13 Find an equation of the normal line to the curve y = 3 sec2 x at the point (z/6,4).tan x tan3 2x sin 3x28.14 Evaluate: (a) lim - (b) lim - (c) lim -x-ro x x-ro x3 x-ro tan 4x