Enter Title

Unit Circle

400

cos(0)

1

800

tan(π/4)

1

1200

sec(π/3)

2

1600

csc(15π)

ø

2000

tan(x) = 5/12

What is cos(x)?

12/13

Solving Trig Equations on [0, 2π)

400

sqrt(3)csc(x) - 2 = 0

π/3, 2π/3

800

sin²(x) + sin(x) = 0

0, π, 3π/2

1200

2sec²(x) + tan²(x) - 3 = 0

π/6, 5π/6, 7π/6, 11π/6

1600

2sin(x) + csc(x) = 0

ø

2000

2cos(2x) - 1 = 0

π/6, 5π/6, 7π/6, 11π/6

Rational Functions

400

What is the vertical asymptote for 

f(x) = 2x² / (x² + 2x + 1)

x = -1

800

What is the horizontal asymptote of

f(x) = (3x³ - 4x + 3) / (4x⁴ - 1)

y = 0

1200

Does the graph of (x + 2) / (x² + 4) have a hole? If so, where?

No.

1600

How many zeros does f have?

f(x) = x / (x² - x - 2)

1 (x = 0)

2000

For f(x) = (x² - 9) / (x² - 2x - 3), give the zeros, HAs, VAs, holes and y-int.

zeros: x = -3

HA: y = 1

VA: x = -1

holes: x = 3 (3, 3/2)

y-int: (0, 3)

Systems of Equations

400

Solve:

x + 0y = 4

0x + y = 2

(4, 2)

800

Solve.

x + 2y = 6

x - 2y = 2

(4, 1)

1200

Solve.

2u + 3v = -1

7u + 15v = 4

(-3, 5/3)

1600

3x - 5y + 5z = 1

2x - 2y + 3z = 0

7x - y + 3z = 0

(1/8, -5/8, -1/2)

2000

Solve. 

(x + 3) / 4 + (y - 1) / 3 = 1

2x - y = 12

Infinite solutions

Miscellaneous

400

If a six-sided die is rolled twice, what is the probability of the sum of the dice being less than 11?

11 / 12

800

log₅(5³⁷⁾

37

1200

Write the partial fraction decomposition for the following:

3 / (x² - 3x)

1 / (x - 3) - 1 / x

1600

What shape has the equation x² + y² = 9

Circle

2000

If f(x) = 1 / sqrt(x + 1), find the limit as h --> 0 of 

(f(x + h) - f(x)) / h

-1 / (2 (x + 1) ^ (3/2))