NAME: MATH237 - EET Trigonometry Test Two EEA October 12, 2018 Complete all your work on engineering paper. Show enough steps so that it is easy to follow your method. Put a rectangle around all final answers. 1. Find O for 0 s O s 360 given that sec 0 = - 2.56 Include a sketch in your solution. [4] 2. Find @ for 3nt s O s 5n given that cos0 =-0.500 Include a sketch in your solution. [4] . The world's largest wind turbine blade is 83.4 m long. It powers an 8 megawatt wind turbine. The blade tip can sustain a velocity of 285 km/h. At that blade tip velocity how fast is the turbine turning? Answer in rpm (revolutions per minute). SHOW ALL CONVERSIONS AND USE v = wr [6] 4 . Sketch one full cycle of the following function. Label axis so that it is possible to see the co-ordinates of five critical values. (Assume all angles are in radians) y = - 5 cos (8(x -)) [5] A function for voltage is given by: V =420 sin 160nt (t in s and V in V) Sketch a graph of V as a function of t for O s t s 0.05 s. Label the axis with amplitude and the start and end points of each cycle. State the frequency of the cycle. [5] 6. The electrical current i (in HA) for a circuit is given by i = 57.8 sin [67(t -0.25) ] MA , where t is time in seconds. (Calculator must be set in radians) [6] a. What is the current at t = 0.392 s? b. Determine one time when the current will be at a maximum. c. What is a value for t for which the current is 45.7 HA?7. Solve for length CB. [6] D 322 m 426 m m A 182 m B LHS=RHS For question 8 use the following identities and work the Left-Hand Side of the given identity until sin0 = - csco COs0 = 1 seco tan0 = - cote tan0 = sino coto = cose cose sine sin 0 + cos20 = 1 1 + tan'0 = sec-0 1 + cot-0 = csc20 8. a) Prove the given identity. tand + coto = secocsco b) Prove the given identity. sece tano cos0 cote [6]