) Determine constants A, B, C, and D so that the graph of y = A· sin(B(x - C)) + D matches the graph...

Question

) Determine constants A, B, C, and D so that the graph of y = A· sin(B(x - C)) + D matches the graph given above. (b) Determine constants A, B, C, and D so that the graph of y = A· cos(B(x - C)) + D matches the graph given above. 2. Evaluate each expression. If any are undefined, write “undefined.” (a) tan(arctan(17)) = (b) cos-1 � cos� 7p 4 ?? = (c) sec� arcsin� 3 5 ?? = (d) sin arccosp 5 5  = (e) sin� sin-1 � 3p 2 ?? = (f) cot� tan-1 � - 3 8 ?? = 3. Rewrite the following expression as an algebraic expression in x. (i.e., no trigonometric functions should be used in your answer.) HINT: Draw a right triangle that has arctan(3/x) as one of its interior angles. sec� arctan� 3 x ?? assuming that x = 3 4. A passenger in an airplane flying at an altitude of 10 kilometers spots two towns directly east of the plane. The angles of depression to the towns are 28? and 55? , respectively. How far apart are the towns? Provide appropriate units.
	
Document Preview: Worksheet #3 MATH 127: Precalculus II 7/18
Name:
Directions:
1) You must write up your solutions individually.
2) Show all work for full credit.
3) Clearly indicate your ?nal answer.
4) Each question is worth 3 points for a total of 15 points.
This worksheet is due on Tuesday, July 25th at 8:00am.
1. Consider the following graph.
(a) Determine constantsA, B, C, and D so that the graph of y =Asin(B(x C))+D matches
the graph given above.
(b) Determine constantsA, B, C, and D so that the graph of y =Acos(B(x C))+D matches
the graph given above.2. Evaluate each expression. If any are unde?ned, write “unde?ned.”
� � ??
7
 1
(a) tan(arctan(17))= (b) cos cos =
4
  
p
� � ??
3 5
(c) sec arcsin = (d) sin arccos =
5 5
� � ?? � � ??
3 3
 1  1
(e) sin sin = (f) cot tan   =
2 8
3. Rewrite the following expression as an algebraic expression in x. (i.e., no trigonometric
functions should be used in your answer.) HINT: Draw a right triangle that has arctan(3=x) as
one of its interior angles.
� � ??
3
sec arctan assuming that x 3
x
4. A passenger in an airplane ?ying at an altitude of 10 kilometers spots two towns directly
 
eastoftheplane. Theanglesofdepressiontothetownsare28 and55 ,respectively. Howfar
apart are the towns? Provide appropriate units.5. In parts (a)-(c), use fundamental trigonometric identities to fully simplify each expression.
There may be more than one correct form of each answer.
  
2 2
(a) sec (x) 1 sin (x)
1
(b)
2
tan (x)+1
2
sec (x)
(c) tan(x) 
tan(x)

David · Accepted Answer

5. (a) sec ^ 2 (x) * {1 – sin^2 (x)}                  [ 1 – sin ^2 (x) = cos ^ 2(x) ] 
= sec ^ 2 (x) * cos ^2 (x) 
= 1 
(b) 1 / ( 1 + tan ^2 (x))                                   [1 + tan ^ 2 (x) = sec ^2 (x)] 
= 1/ sec^2 (x) = cos ^2 (x) 
© tan (x) – { sec^2 (x) / tan ^2 (x)} 
= [tan^2 (x) – sec^2 (x) ]/tan ^2(x) 
= -1/ tan^2( x) = - cot ^2(x)
4 . Let the horizontal distance from the plane of the cars be a and b 
units respectively. 
 tan 55 = 10/a 
 a = 10/tan 55
tan 28 = 10 / b 
 b = 10 / tan 28
b – a = {10/ tan 55} – {10 / tan 28} 
= -(7.04 – 18.86) = 11.82
3. Let the two sides of a right angled triangle be 3 and x 
respectively .

) Determine constants A, B, C, and D so that the graph of y = A· sin(B(x - C)) + D matches the graph given above. (b) Determine constants A, B, C, and D so that the graph of y = A· cos(B(x - C)) + D...

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