We will need to know the following identities and derivatives: sin(p 2 - x) = cos(x) cos(p 2 - x) = sin(x) (sin(x))2 + (cos(x))2 = 1 d dx sin(x) = cos(x) 1. Calculate d dx cos(x) by using the chain...

Math 1105 Winter 2012/2013 Assignment 4 Due Feb 5 at 2:30 pm In this lab, we will calculate the derivatives of trigonometric functions. For testsandexams,youwillhavetoknowallofthesederivativesthatyou will calculate. We will need to know the following identities and derivatives:  sin( x) = cos(x) 2  cos( x) = sin(x) 2 2 2 (sin(x)) +(cos(x)) = 1 d sin(x) = cos(x) dx d 1. Calculate cos(x) by using the chain rule and the trig identities above. dx 2. Write tan(x); sec(x); csc(x); and cot(x) in terms of sin(x) and cos(x): 3. Show that d d 2 tan(x) = sec (x); sec(x) = sec(x)tan(x) dx dx d d 2 csc(x) =csc(x)cot(x); cot(x) =csc (x): dx dx Remember that you know the derivatives of sin(x) and cos(x). 4. Show that 1cos(x) lim = 0: x!0 x (Hint: try multiplying numerator and denominator by 1+cos(x):) Homework Problems Section 2.4 (p119) # 16, 32 Section 2.5 (p124-125) # 18, 34, 48 Section 2.9 (p147) # 12, 30 Section 3.3 (p181-182) # 34, 38, 44 1