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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.
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
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 − 21 a
(a)2a + b
b
b
a
a
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.
−−
→
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.
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?
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Math 151 WIR, Spring 2010, Benjamin
Aurispa
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?
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.
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