The function f (x) = 10 + 2 cos(14x) + cos(11x) + 2 sin(7x) − cos(4x) + 5 cos(3x) is called The Fairy Godmother curve by its shape in polar coordinates. Find the length ||f(x)|| of this curve.

Find the equation of the tangent line T to the graph of f(x) = 8 sinx at the given point (6,8 sin 6). a. y = (8 sin 6)(x+6) + 8cos 6 b. y = -(8cos 6)(x-6) +8sin 6 c. y=(8cos 6x)(x-6) + 8 sin 6 d. y = -(8cos6)(x-6) + 8sin 6 E. y =(8sin6x)(x+6) + 8cos6

() 3. Simplify the expression tan(arcsin (a) V4 – t2 (b) V4+ t? (c) Vt2 + 4 V4 – t? (d) (e) vt2 +4

the pole of (cos(x)-1)/x is...

Which of the following sinusoidal equations has an amplitude of 9, a period of 1080 and a maximum at (0, 1)? f(x) = 9 cos(x) – 8 ○ f(x) = 9 cos (x) + 1 Of(x) = 9 cos(z) f(x) = 9 cos(3x) — 8

The graphs of ƒ(x) = x² – 3x − 4 and g(x) = -2x - 2 intersect at the point (-1,0). The (acute) angle of intersection (in radians) of these graphs at (-1,0) is:

Consider the graph below: MA (0,3) (*, 3) (. 1). .1) (.-1) Which of the functions below might have this as their graph? 2 cos (2x) + 1 2 sin (2x) + 1 2 cos (x) + 1 2 sin (x) + 1 cos (2x) +1 sin (2x) + 1 cos (x) + 1 sin (x) + 1 You rotate by some angle 0 (theta) starting at (1,0). You land at the point (,). Match the trigonometric functions with their values cos(theta) sin(theta) tan(theta) cot(theta) sec(theta) csc(theta)

Differentiate the following: 1. sin@cose 2 csce -cote tan@sece 3 (cos 0-1)0 4 e(2x - 1) 5. x2+ xx3-x