Math 151 WIR, Spring 2010,cBenjamin AurispaMath 151 Week in Review 1Appendix D and Section 1.11. Given that cos θ =14and that3π2< θ < 2π, find cot θ.2. If s in α = −25and tan α > 0, calculate sec α.3. If csc x =43whereπ2< x < π, calculate sin 2x.1Math 151 WIR, Spring 2010,cBenjamin Aurispa4. Solve the following equations on the interval [0, 2π].(a) 2 cos2x = 1(b) sin 2x = − sin x(c) 2 cos2x − sin x = 12Math 151 WIR, Spring 2010,cBenjamin Aurispa5. 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.(a) 2a + b (b) b −12aabab3Math 151 WIR, Spring 2010,cBenjamin Aurispa8. 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.4Math 151 WIR, Spring 2010,cBenjamin Aurispa9. Find a vector−−→AB with initial point A(2, 7) and terminal point B(−3, 9). What is the direction of thisvector 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 ismoving w ith speed 4 km/s due east. Find the true speed and direction of the boat relative to theshore.5Math 151 WIR, Spring 2010,cBenjamin Aurispa12. A plane wants to have a ground speed of 500 miles per hour due north. If the wind is blowing at15 miles per hour in the direction N 45◦W, in what dir ection should the plane head and at whatairspeed?13. Two forces are acting on an object. F1has a magnitude of 30 Newtons and is applied in a directionof 120◦from the positive x-axis. F2has 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 dir ection?(b) What third force F3would be required to keep the object from moving?6Math 151 WIR, Spring 2010,cBenjamin Aurispa14. A 50-lb pi˜nata is being held up between two buildings by two wires. The two wires make angles of60◦and 45◦with the horizontal. Determine the magnitudes of the tension in each
View Full Document
Unlocking...