We will need to know the following identities and derivatives: sin(p 2 - x) = cos(x) cos(p 2 - x) =...

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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 rule and the trig identities above. 2. Write tan(x), sec(x), csc(x), and cot(x) in terms of sin(x) and cos(x). 3. Show that d dx tan(x) = sec2 (x), d dx sec(x) = sec(x) tan(x) d dx csc(x) = - csc(x) cot(x), d dx cot(x) = - csc2 (x). Remember that you know the derivatives of sin(x) and cos(x). 4. Show that limx?0 1 - cos(x) x = 0. (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

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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

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Robert · Accepted Answer

Solution 2013 
 

Question 1: - Calculate 
?
??
 (cos x) by using the chain rule. 
       Solution 1:-  
              We know that, 
                Cos x = Sin (
?
2
−  ?)  
          
?
??
 (Cos x) = 
?
??
 (sin (
?
2
−  ?))
 Here, the outer layer is the sin function, and the inner layer is      
?
2
−  ? .         
Differentiate the sin function first, leaving ( 
?
2
−  ?) unchanged. Then differentiate the (
?
2
−  ?).
          
?
??
 (Cos x) = 
?
??
 (sin (
?
2
−  ?))
                                = 
?
??
 (sin (
?
2
−  ?)). 
?
??
 (
?
2
−  ?)
                         = cos (
?
2
−  ?). (0 - 1)
                         = - cos (
?
2
−  ?)
                         = - sin x 
 
Question 2:- Write tan(x), sec(x), Csc (x) and cot (x) in terms of sin (x) and cos (x). 
Solution 2:-   
a)   Tan(x) = 
sin  (?)
cos  (?)
 
b) Sec(x) = 
1
cos  (?)
 
c)  Csc(x) = 
1
sin  (?)
 
d)    Cot(x) = 
cos  (?)
sin  (?)

Solution 2013 

Question 3:- Show that a)    
?
??
(tan x) = ???2 ?

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...

Answer To: We will need to know the following identities and derivatives: sin(p 2 - x) = cos(x) cos(p 2 - x) =...

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