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Unformatted text preview: MIDTERM 3 SOLUTIONS (CHAPTER 4) MATH 141 FALL 2011 KUNIYUKI 150 POINTS TOTAL: 27 FOR PART 1, AND 123 FOR PART 2 Show all work, simplify as appropriate, and use good form and procedure (as in class). Box in your final answers! No notes or books allowed. PART 1: SCIENTIFIC CALCULATORS ALLOWED! (27 POINTS TOTAL) 1) A central angle of a circle of radius 6 centimeters intercepts an arc of length 3 centimeters along the circle. What is the radian measure of this angle? (4 points) Arc length s = r 3 = 6 ( ) 3 6 = = 1 2 or 0.5 radians 2) Give the solutions for tan = 6 , where < 360 . Give your answers in degrees, and round them off to the nearest tenth of a degree (i.e., to one decimal place). (4 points) In degrees, tan 1 6 ( ) 80.5 . This degree measure is in the specified interval, , 360 ) , so this is one of our solutions. Observe that the corresponding standard angle is in Quadrant I. The only other Quadrant in which tangent is positive in value is Quadrant III. We also want the brother or coreference angle in Quadrant III that is in , 360 ) . The desired brother in Quadrant III is given by about: 180 + 80.5 , or 260.5 . (Intersection points correspond to terminal sides with the same slope, 6.) [Approximate] Solution set: {80.5 o , 260.5 o } 3) Give the solutions for cos = 0.75 , where < 2 . Give your answers in radians, and round them off to the nearest thousandth of a radian (i.e., to three decimal places). (4 points) In radians (the assumed measure), cos 1 0.75 ( ) 2.419 . This is in the specified interval, 0, 2 ) , so this is one of our solutions. Observe that the corresponding standard angle is in Quadrant II. The only other Quadrant in which cosine is negative in value is Quadrant III. We also want the brother or coreference angle in Quadrant III that is in 0, 2 ) . The desired brother in Quadrant III is given by about 2 2.419 , or 3.864....
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This note was uploaded on 02/07/2012 for the course MATH 2203 taught by Professor Ellermeyer during the Fall '10 term at FIU.
 Fall '10
 Ellermeyer
 Math

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