Force A at 100 pounds and force B at 120 pounds make an angle of with each

# Force a at 100 pounds and force b at 120 pounds make

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Force A , at 100 pounds, and force B , at 120 pounds, make an angle of with each other. Represent their respective vectors as complex numbers written in trigonometric form, and solve for the resultant force. 60. Resultant Force. Force A , at 40 pounds, and force B , at 50 pounds, make an angle of with each other. Represent their respective vectors as complex numbers written in trigonometric form, and solve for the resultant force. 45° 100 lb Force A 120 lb Force B 30º 30° 61. Resultant Force. Force A , at 80 pounds, and force B , at 150 pounds, make an angle of with each other. Represent their respective vectors as complex numbers written in trigonometric form, and solve for the resultant angle. 62. Resultant Force. Force A , at 20 pounds, and force B , at 60 pounds, make an angle of with each other. Represent their respective vectors as complex numbers written in trigonometric form, and solve for the resultant angle. 63. Resultant Force. Refer to Section 8.4, Exercise 85. Express the vectors corresponding to the dogs as complex numbers written in trigonometric form, and find the resultant force to keep the system in equilibrium. 64. Resultant Force. Refer to Section 8.4, Exercise 86. Express the vectors as complex numbers written in trigonometric form, and find the resultant force to keep the system in equilibrium. 65. Resultant Force. Refer to Section 8.4, Exercise 75. Express the resultant vector as a complex number in trigonometric form. 66. Resultant Force. Refer to Section 8.4, Exercise 76. Express the resultant vector as a complex number in trigonometric form. R S R S z S u S , v S , w S w S u S , v S 60° 30° 67. Express in polar form. Solution: Find r . Find Write the complex number in polar form. This is incorrect. What mistake was made? z = 1 73 (cos 69.44° + i sin 69.44°) u = tan - 1 a 8 3 b = 69.44° tan u = 8 3 u . r = 2 x 2 + y 2 = 1 9 + 64 = 1 73 z = - 3 - 8 i 68. Express in polar form. Solution: Find r . Find Write the complex number in polar form. This is incorrect. What mistake was made? z = 1 73 [cos( - 69.44°) + i sin( - 69.44°)] u = tan - 1 a - 8 3 b = - 69.44° tan u = - 8 3 u . r = 2 x 2 + y 2 = 1 9 + 64 = 1 73 z = - 3 + 8 i In Exercises 67 and 68, explain the mistake that is made. 69. In the complex plane, any point that lies along the horizontal axis is a real number. 70. In the complex plane, any point that lies along the vertical axis is an imaginary number. 71. The modulus of z and the modulus of are equal. 72. The argument of z and the argument of are equal. 73. Find the argument of where a is a positive real number. z = a , z z 74. Find the argument of where b is a positive real number. 75. Find the modulus of where b is a negative real number. 76. Find the modulus of where a is a negative real number. In Exercises 77 and 78, use a calculator to express the complex number in polar form. 77. where 78. where a 7 0 - 3 a - 4 ai , a 7 0 a - 2 ai , z = a , z = bi , z = bi , A P P L I C AT I O N S C ATC H T H E M I S TA K E C O N C E P T U A L In Exercises 69–72, determine whether each statement is true or false. 914 CHAPTER 8 Additional Topics in Trigonometry Graphing calculators are able to convert complex numbers from rectangular to polar form using the abs command to find the modulus and the angle command to find the angle.  #### You've reached the end of your free preview.

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• Summer '17
• juan alberto
• Complex Numbers, Sin, Cos, Complex number
• • • 