Unit Circle & Trig
Polar
Vectors
Sequences
Limits
100
sin((-7pi)/6)=?
1/2
100
Give the coordinates of this point
(6, (3pi)/4)
100
Give the vector in component form with the initial point
(-2,-12)
and terminal point
(9,-7)
⟨11,5 ⟩
100
The 15th term of the sequence:
a_n=6n^2-4
1346
100
lim_(x→3)x^2-3x+1
1
200
Give the period of the graph of
-3sin(pi/2)+1
4pi
200
Give another representation of the point
(3,(5pi)/6)
with r<0
(-3,(11pi)/6)
200
Give the magnitude of the vector
vecv=-10i-j
|v|=sqrt101approx10.05
200
Give the nth term of the sequence:
1/2,4/3,9/4,16/5,25/6,...a_n
a_n=n^2/(n+1)
200
lim_(x→0)f(x)
2
300
What is the phase shift of the graph
1/2cos(2theta-pi/4)
pi/8
300
What shape does this equation make?
r=3+sin(6theta)
Rose
300
Give the direction of the vector
vecu=7i-15j
thetaapprox295^o
300
sum_(k=3)^6 k^2-k
68
300
lim_(x→-∞)x^2-3x+2
oo
or DNE
400
Simplify this expression completely:
costheta/(1+sintheta)+costheta/(1-sintheta)
2sectheta
400
Give another representation of
(-5,(5pi)/3)
with r>0 and θ <0
(5,-(4pi)/3)
400
Give the direction from the y-axis of the vector
vecw=⟨ 2,-5,21 ⟩
betaapprox103.3^o
400
An arithmetic sequence has a 19th term of -181 and a 42nd term of -434. Find the sum of the first 120 terms.
S_120=120/2(17-1292)=-76500
400
lim_(x→oo)(1-x^2)/(-x+x^2+2x^3)
0
500
Solve for θ :
sintheta-2cos^2theta=-2
theta={0,pi,(7pi)/6, (11pi)/6}+2pik
500
Convert this point to polar coordinates
(-6sqrt3,18)
(12sqrt3, (2pi)/3)
or
(20.8,120^o)
500
A bird flies S 30o W at a speed of 40 mph. At some point in the migration, the bird catches a tailwind of 25 mph blowing in the south direction. What is the real speed and direction of the bird at this moment?
True speed: 62.9 mph
Real direction: 251.5o (or S 18.5o W or W 71.5o S)
500
Find the sum of the partial sequence shown:
5,10,20,40,...327680
655355
500
lim_(x→-1)(x^3-3x^2-4x)/(2x^2+x-1)
-5/3