Precalculus

Question 1

Pythagorean Identity

Answer 1

sin²x + cos²x = 1

Question 2

Pythagorean Identity (Tangent)

Answer 2

1 + tan²x = sec²x

Question 3

Pythagorean Identity (Cotangent)

Answer 3

1 + cot²x = csc²x

Question 4

Sum Formula (Sine)

Answer 4

sin(A + B) = sinAcosB + sinBcosA

Question 5

Sum Formula (Cosine)

Answer 5

cos(A + B) = cosAcosB - sinAsinB

Question 6

Difference Formula (Sine)

Answer 6

sin(A - B) = sinAcosB - sinBcosA

Question 7

Difference Formula (Cosine)

Answer 7

cos(A - B) = cosAcosB + sinAsinB

Question 8

Quotient Identity

Answer 8

tan x = sin x / cos x

Question 9

Reciprocal Identity (Cotangent)

Answer 9

cot x = 1 / tan x

Question 10

Reciprocal Identity (Cosecant)

Answer 10

csc x = 1 / sin x

Question 11

Reciprocal Identity (Secant)

Answer 11

sec x = 1 / cos x

Question 12

Criteria for Continuity

Answer 12

1. f(c) exists
2. lim (x->c) f(x) exists
3. lim (x->c) f(x) = f(c)

Question 13

Jump Discontinuity

Answer 13

lim (x->a^-) f(x) != lim(x->a⁺) f(x)

Question 14

Essential (Infinite) Discontinuity

Answer 14

Occurs where there is a vertical asymptote

Question 15

Point Discontinuity

Answer 15

lim(x->a) f(x) != f(a)

Question 16

Removable Discontinuity

Answer 16

Common factors in numerator and denominator