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Math 021 MATH - 1022 Test 3/100 points Spring 2021 Due by Saturday, April 10, 2021 @ 11:59pm. Directions: Please do your own work. Do not solicit help from anywhere or anyone or from any other source or classmates to help you with the Test. You could use you textbook, notes and any other online sites to help you familiarize with the topics, but do not directly use these questions to seek assistance. You may use a scientific calculator. Please show all work completely. Once done, please send it to me via email (
[email protected]) in PDF form with “Test 3 Math 1022_your name” as the subject. Ensure that all problems are done in order and your Test is legible. Name: _________________________________ 1) Given 2 i− + , convert to trigonometric form, where 3600 <≤ θ="" 2)="" given="" vector="" v="">< -2,="" 15="">, find the magnitude and the direction angle. mailto:
[email protected] 3) Find the angle between the vectors: a = 3 4i j+ and 2b i j= − − . 4) Use Demoivre’s theorem to find 5( 1 2 )i− − . Hint: )]sin()[cos( θθ ninrZ nn += 5) Find the work done when a constant force F is applied to an object that moves along the Vector D, where units are in lbs and feet. F = 4i -24j D= -2i+5j 6) Perform the indicated operation and record your answer in rectangular form. a) 3 34 cos sin 5 cos sin 4 4 4 4 i iπ π π π + + b) ( ) ( ) + + 100sin100cos2 200sin200cos4 i i 7) Find the fifth roots for 16 16 3i− − 8) Sketch the graph of the polar equation 3sinr θ= 9) Find the parametric equations for the curve with the line with slope -2 passing through (-10, -20) 10) Find the area of a triangle PQR∆ (2,1,0), (0,0, 1), ( 4, 2,0)P Q R− −