Math 151 WIR Spring 2010 c Benjamin Aurispa Math 151 Week in Review 1 Appendix D and Section 1 1 1 Given that cos 1 4 and that 3 2 2 find cot 2 If sin 25 and tan 0 calculate sec 3 If csc x 4 3 where 2 x calculate sin 2x 1 Math 151 WIR Spring 2010 c Benjamin Aurispa 4 Solve the following equations on the interval 0 2 a 2 cos2 x 1 b sin 2x sin x c 2 cos2 x sin x 1 2 Math 151 WIR Spring 2010 c Benjamin Aurispa 5 Sketch a graph of the function y 3 sin 2x 6 Sketch a graph of the function y cos x 4 2 7 Represent geometrically the following vectors b b 12 a a 2a b b b a a 3 Math 151 WIR Spring 2010 c Benjamin Aurispa 8 Consider the vectors a 5 6 b 4i j and c 3 2 Calculate the following a a 2b j b b 3c c A unit vector in the direction of a d A vector with length 4 in the opposite direction of c e Find constants s and t so that sa tb c 4 Math 151 WIR Spring 2010 c Benjamin Aurispa 9 Find a vector AB with initial point A 2 7 and terminal point B 3 9 What is the direction of this vector from the positive x axis 10 Find a vector with length 12 and direction 210 from the positive x axis 11 A boat is moving with speed 36 km s relative to the water in the direction N 60 E The water is moving with speed 4 km s due east Find the true speed and direction of the boat relative to the shore 5 Math 151 WIR Spring 2010 c Benjamin Aurispa 12 A plane wants to have a ground speed of 500 miles per hour due north If the wind is blowing at 15 miles per hour in the direction N 45 W in what direction should the plane head and at what airspeed 13 Two forces are acting on an object F1 has a magnitude of 30 Newtons and is applied in a direction of 120 from the positive x axis F2 has a magnitude of 40 Newtons and is applied in a direction of 30 from the positive x axis a What is the resultant force F as well as its magnitude and direction b What third force F3 would be required to keep the object from moving 6 Math 151 WIR Spring 2010 c Benjamin Aurispa 14 A 50 lb pin ata is being held up between two buildings by two wires The two wires make angles of 60 and 45 with the horizontal Determine the magnitudes of the tension in each wire 7
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