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c Math 151 WIR, Spring 2010, Benjamin Aurispa Math 151 Week in Review 1 Appendix D and Section 1.1 1. Given that cos θ = 1 4 and that 3π 2 < θ < 2π, find cot θ. 2. If sin α = − 25 and tan α > 0, calculate sec α. 3. If csc x = 4 3 where π 2 < x < π, calculate sin 2x. 1 c Math 151 WIR, Spring 2010, Benjamin Aurispa 4. Solve the following equations on the interval [0, 2π]. (a) 2 cos2 x = 1 (b) sin 2x = − sin x (c) 2 cos2 x − sin x = 1 2 c Math 151 WIR, Spring 2010, Benjamin Aurispa 5. Sketch a graph of the function y = −3 sin(2x). 6. Sketch a graph of the function y = cos(x + π4 ) − 2. 7. Represent geometrically the following vectors. (b) b − 12 a (a) 2a + b b b a a 3 c Math 151 WIR, Spring 2010, 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 c Math 151 WIR, Spring 2010, 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 c Math 151 WIR, Spring 2010, 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 c Math 151 WIR, Spring 2010, Benjamin Aurispa 14. A 50-lb piñata 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