Chapter 5. Section 5.1. Section ( x ) ( y ) 7. ( x ) ( y ) (0, 3 + 5) and (0, 3 5)

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1 9 Chapter Section.. 0. ( x ) ( y ). ( x 7 ) + ( y+ ) = 9 7. ( x ) ( y ) = = 9.. (0, + ) and (0, ). (.60786, ). (-.07,.8) miles Section miles 7. 8 cm miles cm. 960 rad/min 60. RPM in/sec, / rad/sec,. RPM 9. 7,98. mm/min =.7 m/sec. Angular speed: / rad/hr. Linear speed: 06.7 miles/hr

2 0 Section.. a. III b. II a. reference:. Quadrant III. sin ( ) =. cos( ) 8 = cos 00 = cos = cos 0 = b. reference: 60. Quadrant IV. sin ( 00 ) =. ( ) c. reference:. Quadrant II. sin ( ) =. ( ) d. reference: 0. Quadrant III. sin ( 0 ) =. ( ). a. reference:. Quadrant III. sin =. cos = 7 7 b. reference:. Quadrant III. sin =. cos = c. reference:. Quadrant IV. sin =. cos = d. reference:. Quadrant II. sin =. cos =. a. sin = cos = b. sin = cos = 6 6 c. sin = cos = 0 cos = d. sin ( ) 0 = ( ). a. 7. a. b. 00 c. 0 d. b. 80 c. 0 d. e. e. 9. (-.9, -9.6)

3 Section.. sec( θ ) =, csc( θ ) =, tan ( θ ) =, ( ) cot θ =. sec( θ ) =, csc( θ ) =, tan ( θ ) =, ( ). sec( θ ) =, csc( θ ) =, tan ( θ ) =, cot ( ) cot θ = θ = 7. a. sec( ) = b. csc( 0 ) = c. tan ( 60 ) =. d. ( ) cot = cos( θ ) =, sec( θ ) =, csc( θ ) =, tan ( θ ) =, cot ( ) 7 7 θ = 7. sin ( θ ) =, csc( θ ) =, sec( θ ) =, tan ( θ ) =, cot ( ). sin ( θ ) =, cos( θ ) =, sec( θ ) =, csc( θ ) =, cot ( ) θ =. a. sin(0.) = 0.9 cos(0.) = tan(0.) = 0. b. sin() = cos() = tan() =.78 c. sin(70 ) = cos(70 ) = 0.0 tan(70 ) =.77 d. sin(8 ) = cos(8 ) = 0.0 tan(8 ) = sec( t ) 9. tan( t ). tan( t ). cot( ) t. ( sec( t )) θ = Section. sin ( A) =,cos( A) =, tan( A) =. sec ( A ) =,csc( A) =,cot( A) =. c=, b= 7, B= 60. a =.7, c=.7, A= 8 7. a = 9.06, b=.6, B= ft ft ft feet ft

4 Chapter 6 Section Amp:. Period=. Midline: y= -. f ( t) ( t) = sin = cos t + = cos t 6. Amp:. Period=. Midline: y= -. f ( t) = sin t 7. Amp:. Period=. Midline: y=. f ( t) 8. Amp:. Period=. Midline: y= -. f ( t) ( ) 9. Amp:. Period=. Midline: y=. f ( t) 0. Amp:. Period=. Midline: y= -. ( ) = cos t + f t = sin t. Amp:, Period =, Shift: left, Midline: y =. Amp:, Period =, Shift: right, Midline: y = 7. Amp:, Period =, Shift: 7 right, Midline: y =

5 . Amp:, Period =, Shift: left, Midline: y = -. Amp:, Period =, Shift: 6 left, Midline: y = - 6. Amp: 8, Period = 7, Shift: left, Midline: y = 6 8. f ( x) = sin ( x+ ) 9. f ( x) = cos ( x+ ) 0. f ( x) = cos ( x ). Dt ( ) = 0 7sin t. Dt ( ) = 68 sin t. a. Amp:.. Midline: y =.. Period: 0 b. ht ( ) =.cos t +. c. h ( ) = 6 meters. a. Amp: 7.. Midline: y = 0.. Period: 8 b. h( t) = 7.cos t + 0. h = meters 7. f ( x) = sin ( x+ ) c. ( ) 8 Section 6.. II. I. Period:. Horizontal shift: 8 right 7. Period: 8. Horizontal shift: left 9. Period: 6. Horizontal shift: left

6 ... = 7. f ( x) sec x 9. f ( x) = csc x +. tan ( x) =.. ( x). csc( x) = 7. csc( x) sec = Section x x 9x

7 Section 6.., 7., k, + k, where k is an integer. 7, + k + k, where k is an integer k, + k, where k is an integer k, 7 + k, where k is an integer 7. + k, + k, where k is an integer k, + k, where k is an integer. + 8k, where k is an integer. + k, + k, where k is an integer ,. 0.7, , , , , , , ,.69 Section 6.. c = 89, A = 7.996, B =.00. b = 7 6, A = 7.88, B = y( x) = 6sin ( x ) + 7. D( t) = 0 cos ( t ) 9. a. P( t) = 9 cos t P t = t degrees months b. ( ) 9 cos ( )

8 6 Chapter 7 Section 7.. 7, 6 6.,. + 8k, and 0 + 8k, where k is an integer 7. + k and 7 + k, where k is an integer k and k, where k is an integer..8 + k and k, where k is an integer.,, 0.6, ,.,.97, ,,, 9.,,, ,.98,.,.00., 7, 6 6.,, 7..8, ,.98, 0.7,.60..0, ,,,,,. 7.,,, 6 6., Section ,,,,, 9. 0,,.,

9 7 9. sin ( x) cos( x). cos( x) + sin ( x). sec( t ). tan ( x ) ( ) 7. 8 cos( x) cos( 7x) 9. sin ( 8x) + sin ( x). cos( t) cos( t ). sin ( x) cos( x ). a. + = b. + + = k and k, where k is an integer 9. k, where k is an integer k, k, + k, and k, + k, and k k, where k is an integer. sin( x +.00) or sin( x 0.988) 7. 9sin(x ) , ,.88. tan ( 6t ), where k is an integer Section 7.. a. 7 b. c. 7. cos( 6 ). cos( ) 7. cos( 8x ) 9. sin ( 6x ). 0,,.89, ,.9,.87,.

10 8.,,, a ,,,,,,0,, ( x) + cos cos( 6x) + cos( x) cos( x) + cos( x) cos( x) cos ( x). a. + b. 7 c. 7 7 Section 7. = sin 6. y ( x ). Amplitude: 8, Period: second, Frequency: Hz (cycles per second) 0 P t = 9 cos t + t ( ) 6 t 7. P( t) = cos t + 900(.07) t 9. D( t) = 0( 0.8) cos(6 t). D( t) = 7( 0.9) t cos( 8 t). a. IV b. III. y ( ) x = 6 + sin x 7. y = sin + x+ 7 x 9. y = 8 cos x +

11 9 Chapter 8 Section β = 68, a =.7, c = 0.8. β = 8.096, γ =.90, c = 6.9. Not possible.. β = 6., γ = 7.67, c = 7.8 OR β =.77, γ =., c = c =.066, α =., β = 86.. a =.69, β = 7.7, γ = ft 9. Distance to A: 6.8 ft. Distance to shore:.69 ft. 9.0 m feet..6 km,.79 km ft miles. 6.7 cm. 7.7

12 0 Section ,. (, ). (, ) 7. (0,) 9.,. (.8,.78). (, 0.6 ). (,.9 ) 7. (,. ) 9. ( 69,.07 ). r = sec( θ ). = 7.. r sin ( θ ) 9. x y y sin r = cos r = + =. y+ 7x= ( θ ) ( θ ) cos( θ ) ( θ) sin ( θ) ( cos ). x =. x + y = x+ 7. A 9. C. E. C. D 7. F

13 Section 8.. i.. + i 7. 8 i 9. + i. + 8i. 0 0i. + 0i i. + i. 8 i. 7. i cos + sin i = i 9. ( ) ( ). + i.. 0 6e i 7. e i e i 9. i. e 0.0i. e. 0e e.67i e 9. i i. e 6e 7 i e i i.80i 6.086i. 0e i i 6..9, i, i, i, i 67., + i, + i,, i, i

14 Section 8..,. The vectors do not need to start at the same point. v u 7., ,.. Magnitude:, Direction: 90. Magnitude: 7.80, Direction: Magnitude:.6, Direction:. 7. Magnitude:.8, Direction: Magnitude: 7., Direction: 6.0. u + v =,, u v =, 8, u v =,..6 miles, 7.76 deg N of E. 7 miles. 0.8 miles 7. F net =, 9. Distance:.868. Direction: 86.7 North of West, or.6 West of North..9 degrees. 69 km/hr.. degrees. (0.08, 8.60) degrees, relative to the car s forward direction

15 Section 8.. C. E. F x(t) y(t).. y = + x. y x 7. x= e or y = ln 9.. y = x.. ( ) t ( ) t xt = y t = + 7. x y = y y x = x y + = ( ) log ( ) ( ) = t xt = t+ t. y t

16 ( ) cos( t) ( ) = sin ( t) xt = y t xt y t ( ) = t ( ) = t ( ) cos( t) ( ) = 6sin ( t) xt = y t. y( x) x x = ( ) ( ) xt = t. y t = t+ x( t) = + t. y( t) = t xt ( ) = cos( t) 9. y( t) = sin ( t) xt ( ) = 0sin t + 8sin ( t). y t = 0 cos t 8cos t ( ) ( )