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Ch 7-Analytic Trig
Ch 8-Applications of trig
Ch 9-Polar coordinates and vectors
Ch 12-Sequences
Ch 10-Analytic Geometry
100
Find the exact value of sin-1(√2 / 2)
π/4
100
Find the exact value without using a calculator: tan(20°) - cos(70°) / cos(20°)
Use the complement angle theorem to let cos(70°) = sin(90°-70°) = sin(20°)
100
The polar coordinates are given. Convert to rectangular: (7.5, 110°)
(-2.57, 7.05)
100
Find the sum: ∑(3k) from k=1 to 5
45
100
Find the vertex, directrix, and vertex: y^2 - 4y +4x +4 = 0
Directrix: x=1 Focus: (-1, 2) Vertex: (0, 2)
200
Find the exact value: sin-1[cos(-7π/6)]
-π/3
200
What is the law of sines?
SinA/a = sinB/b = sinC/c
200
What shape does this polar graph make? r=a+-bcosx or r=a+-bsinx
Limacon with inner loop.
200
Find the first term, common difference, and recursive for the arithmetic sequence: the 9th term is -5 and the 15th term is 31.
a1 = -53, d=6, an = a(n-1) + 6
200
Find the verticies, center, and foci of the ellipse: 4x^2 + y^2 + 4y = 0
Verticies: (0,-4),(0,0) Center: (0,-2) Foci: (0, -2-√3),(0,-2+√3)
300
Solve on 0
x = 3π/4, 7π/4
300
Solve the triangle: A=40°, B=40°, c=2(side)
C=100°, a~1.31, b~1.31
300
Graph: r=4sin(5x)
Rose with 5 petals.
300
Define an arithmetic sequence.
a1=a, an = a(n-1) + d
300
Find an equation for this ellipse. Center at (1,2), focus at (4,2), contains the point (1,3).
[ ( (x-1)^2 ) / 10 ] + (y-2)^2 = 1
400
Find the exact value: If tan(x)= -1/2 and 3π/2 < x < 2π , find sin(2x).
-4/5
400
Which triangle cases are solved by the law of cosines? (Hint: in reference to ASA, SAS, SAA, SSS, etc.)
SAS, SSS
400
What is De Moivre's theorem?
z^n = r^n[cos(nx)+isin(nx)]
400
Define: the nth term of a geometric sequence.
An = a1r^(n-1) r cannot equal zero.
400
Find an equation for the hyperbola: center at (4,-1), focus at (7,-1), and vertex at (6,-1)
[((x-4)^2) / 4] - [((y+1)^2) / 5] = 1
500
Establish the identity: cos^4(x) - sin^4(x) = cos(2x)
Cos(2x) = cos^2(x) - sin^2(x) and cos^4(x) - sin^4(x) can be simplified to (cos^2(x) - sin^2(x)) * (cos^2(x) + sin^2(x)) then you can divide the common terms to establish the identity.
500
Solve the triangle: a=10, b=8, c=5 (SSS)
A=97.9°, B=52.4°, C=29.7°
500
Write in the standard form a+bi: [√5 (cos(3π/16) + isin(3π/16)]^4
(- 25√2 / 2) + (25√2 / 2)(i)
500
Does the sequence converge or diverge? ∑5[(1/4)^k-1] from k=1 to infinity.
converges
500
Find the center, transverse axis, verticies, foci, and asymptotes of the hyperbola. [(y-2)^2] - 4[(x+2)^2] = 4
Center: (-2,2) Transverse Axis: parallel to the y-axis Verticies: (-2,0),(-2,4) Foci: (-2, 2-√5),(-2,2+√5) Asymptotes: y-2= ±2(x+2)