Download McLoughlin P-Final Math 120 Fall-13 Name: 1.) (9 points) Find the

McLoughlin
P-Final Math 120 Fall-13
Name:
1.) (9 points) Find the amplitude, period, phase shift, and vertical shift then sketch the graph.
y = 4cos(5x − 7) − 8
2.) (8 points) Solve ∆ABC given α = 45◦ , b=15, and c=12.
3.) (8 points) A 10 foot beam supports a tilted wall. The angle the beam makes with the ground
is 60◦ and the wall makes a 87◦ angle with the ground. Find the distance the base of the beam is
from the base of the wall.
4.) Let V=(2,-5) and W=(-1,4). Find the following (2.5 points each):
a.) 3V-5W
b.) kW k
c.) V · (3V − 5W )
d.) The angle between V and W .
5.) (8 points) Verify the identity.
sin4t = 4(sint)(cost)(1 − 2(sint)2 )
6.) (8 points) Use sum-to-product formulas to find the solution of the equation.
sin(5t + π2 ) − sin(t + π7 ) = 0
7.) Find the exact value(3 points each).
7
7
a.) sin(arctan 12
)
b.) sin(4arctan 12
)
x
)
c.) cos(arcsin x+1
8.)(8 points) Find the three cube roots of 1 + i.
9.) (8 points) Write decimal as a fraction in lowest terms.
.14565
10.)(8 points) Prove statement using induction.
9
18 + 28 + 38 + . . . n8 < (n+1)
9
11.) (8 points) Use the binomial Theorem to find the fifth term of (3x2 −
√
y)7 .
12.) (8 points) Find vertex, focus, and directrix of the parabola then sketch graph.
9x2 − 5x + 9 − 2y = 0
2