ENGR 1990 Engineering Mathematics
Lab/Recitation #7: Test II Review – Geometry, Trigonometry, Vectors, and Complex Numbers
1. Given: x = 5 (in), y = 2 (in)
Find: r, θ, φ
φ
r
y
θ
2. Given: r = 10 (in), θ = 30 (deg)
Find: x, y, φ
x
3. Given: r = 10 (in), θ = 120 (deg)
Find: x, y
(x, y)
4. Given: x = 10 (in), y = 3 (in)
Find: r, θ
r
θ
5. Given: x = -10 (in), y = 6 (in)
Find: r, θ
6. Given: 1  8 (in) ,  2  10 (in) , 1  30 o ,  2  20o
Find: x, y
(x, y)
7. Given: 1  8 (in) ,  2  10 (in) , x  7 (in) , y  5 (in)
Find:  the elbow angle
θ2
(x, y)
θ1
elbow
IC
8. Given: The coordinates (in inches) of
Y
points A, B, and C and the velocity of B:
A: (0, 2)
B: (5, 5)
C: (12,0)
vB  5 (in/s) in direction shown
Find:  . Then, using the right triangle
ADIC, find r B , rC and vC the velocity
of C.
BC 
B
A
D
X
vB vC

(radians/sec)
rB rC
C
IC
Y
9. Given: The coordinates (in inches) of points
A, B, and C:
A: (0, 2)
B: (5, 5)
C: (12,0)
Find: the angles  ,  ,  ,  , and  .
Find: the lengths r B and rC using the law of sines
B
b
A
X
C
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10. Given: | F1 | 100 (lb) at 60 (deg), | F2 | 200 (lb) at 150 (deg)
Find: F1 , F2 , F  F1  F2 , magnitude and direction of F
11. Given: A  10 i  3 j , B  5 i  8 j
Find:  the angle between the two vectors
12. Given: F  2 i  10 j (lb) , y  12   86  x
Find: a) n a unit vector parallel to the line, b) F the component of F parallel to the line, and c) F
the component of F perpendicular to the line.
13. Given: F  50 i  150 j (lb) applied at A (10, 0) (ft)
Find: a) M B the moment of the force about point B (3, 5) (ft) , b) d the perpendicular distance from
B to the line of action of F .
14. A block of weight W is held in place against a
frictionless inclined plane by the horizontal force
P . The plane exerts only a normal force N on the
block. The weight of the block is | W |  275 (lbs)
and the inclination angle is   60 o
a) Express the forces W and P in terms of the unit vectors i and j .
b) Find the force P and the normal force N so that P  W  N  0 .
15. A voltage v(t )  110 cos(120 t ) is applied to an RLC series circuit with
R  150 (ohms) , L  500 (mh) , and C  100 (f) . The impedance of the circuit is
Z eq  Z R  Z L  Z C .
a) Z eq in both rectangular and polar form
b) I the complex current in both rectangular and polar form
c) i (t ) the current as a function of time
16. A voltage v (t )  110 cos(120  t ) volts is applied to the RL parallel
circuit with R  200  and L  250 mh . Given that the equivalent
Z Z
impedance is Z eq  R L , find
ZR  ZL
a) Z eq in both rectangular and polar form
b) I the complex current in both rectangular and polar form
c) i (t ) the current as a function of time
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