Math 151 WIR, Spring 2014, c Benjamin Aurispa
1. Find the domain of the function f ( x ) = √ x
√ x + 3
2 − 3 x − 4
.
2. Given that cos θ = − 1
4 and that π < θ < 2 π , find csc θ .
3. If cot x = − 5
3 where π < x < 2 π , find sin 2 x .
4. Solve the following equations on the interval [0 , 2 π ].
(a) 2 cos 2 x = 1
(b) sin 2 x = − sin x
(c) 2 sin 2 x + sin x − 1 = 0
5. Using the figures below, sketch the following vectors.
(a)2 a + b (b) b − 1
2 a b b a a
6. Consider the vectors a = < 5 , − 6 >, b = − 4 i − j , and c = < − 3 , 2 > . Calculate the following.
(a) a + 2 b − j
(b) | b − 3 c |
(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 s a + t b = c .
7. Find the vector
−−→ with initial point A ( − 3 , 7) and terminal point B (2 , 5). What is the direction of this vector from the positive x -axis?
8. Find a vector with length 12 and direction 210 ◦ from the positive x -axis.
9. A plane heads in the direction N 60 ◦ E with an airspeed of 500 mph. The wind is blowing due west with speed 10 mph. Find the true speed and direction of the plane relative to the ground.
10. Two forces are acting on an object.
F
1 has a magnitude of 30 Newtons and is applied in a direction of 120 ◦ from the positive x -axis.
F
2 has a magnitude of 40 Newtons and is applied in a direction of
− 30 ◦ from the positive x -axis. What is the resultant force F as well as its magnitude and direction?
30 ◦ and 45 ◦ with the horizontal. Determine the magnitudes of the tension in each wire.
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