Math
Really, this is a lower priority than the other parts of the
website, but there are a few things I should put up now.
Due to the Daily Universe Article being put onto lds.org, many people (from around the world) have emailed
me about teaching calculus using the scriptures. The text I use is Calculus by Lynn E. Garner, Brigham
Young University. I therefore arranged
the scriptures by topic as they arose in my text. I have at least one scripture for each day, so many topics will
have two scriptures (and some more when I could not leave some out). Recently, students have been bringing in
their own because they are now seeing connections as they study the scriptures.
Teaching Calculus 1 through the Scriptures
Teaching Calculus 2 through the Scriptures
Math/Scripture
Items Shared with me from around the world
Algebraic
Properties of Equality
Algebraic
Properties of Inequality
Trigonometric Definitions, Properties, Formulas, and Laws
Definitions
|
Function |
Symbol |
Right Triangle |
Unit Circle |
Any Circle |
|
sine |
sinq |
Opposite over Hypotenuse |
y |
y/r |
|
cosine |
cosq |
Adjacent over Hypotenuse |
x |
x/r |
|
tangent |
tanq |
Opposite over Adjacent |
y/x |
y/x |
|
cotangent |
cotq |
Adjacent over Opposite |
x/y |
x/y |
|
secant |
secq |
Hypotenuse over Adjacent |
1/x |
r/x |
|
cosecant |
cscq |
Hypotenuse over Opposite |
1/y |
r/y |
Reciprocal Identities
|
cotq = 1/tanq |
secq = 1/cosq |
cscq = 1/sinq |
Quotient Identities
|
tanq = sinq/cosq |
cot q = cosq/sinq |
Pythagorean Identities
|
sin2q + cos2q = 1 |
tan2q + 1 = sec2q |
cot2q + 1 = csc2q |
Reduction Formulas
|
sinq = -sin(q-π) |
cosq = -cos(q-π) |
tanq = tan(q-π) |
|
sin(-q) = -sinq |
cos(-q) = cosq |
tan(-q) = -tanq |
|
sinq is odd |
cosq is even |
tanq is odd |
Periodicity and Complement Formulas
|
sin(q + n2π) |
= sinq = |
cos(q - π/2) = cos(π/2 - q) |
|
cos(q + n2π) |
= cosq = |
sin(q + π/2) = sin(π/2 - q) |
|
tan(q + nπ) |
= tanq = |
-cot(q - π/2) = cot(π/2 - q) |
Sum and Difference Formulas
Law of Sines
Double, Reduction, and Half-Angle Formulas
Law of Cosines
Algebraic
Properties of Equality
If a, b, c, and d ε R, then
Reflexive Property a = a
Symmetric
Property If a = b, then b = a
Transitive
Property If a = b and b = c,
then a = c
Addition
Property If a = b, then a + c =
b + c
Addition
Property If a = b and c = d,
then a + c = b + d
Subtraction
Property If a = b, then a - c =
b - c
Subtraction
Property If a = b and c = d,
then a - c = b - d
Multiplication
Property If a = b, then ac = bc
Multiplication
Property If a = b and c = d,
then ac = bd
Division
Property If a = b and c ≠
0, then a/c = b/c
Commutative Property of Addition a + b = b + a
Commutative Property of Multiplication ab = ba
Associative Property of Addition a + (b + c) = (a + b) + c
Associative Property of Multiplication a(bc) = (ab)c
Distributive Property over Addition a(b + c) = ab + ac
Distributive Property over Subtraction a(b - c) = ab - ac
Cancellation Law for Addition If a + b = a + c, then b = c
Cancellation Law for Multiplication If ab = ac and a ≠ 0, then b = c
Substitution
Property If a = b, then b may
be substituted for a in any equation
Algebraic Properties of Inequality
If a, b, c, and d ε R, then
Transitive Property If a < b and b < c, then a < c
Addition
Property If a < b, then a + c
< b + c
Addition
Property If a < b and c < d,
then a + c < b + d
Subtraction
Property If a < b, then a - c
< b - c
Subtraction
Property If a < b and c >
d, then a - c < b - d
Multiplication
Property If a < b and c >
0, then ac < bc
Multiplication
Property If a < b and c <
0, then ac > bc
Division
Property If a < b and c >
0, then a/c < b/c
Division
Property If a < b and c <
0, then a/c > b/c
Identities
and Inverses
If a ε R, then
R has an additive identity called 0 where a + 0 = a
R has a
multiplicative identity called 1 where a
· 1 = a
R has an
additive inverse (the negative) where a
+ (-a) = 0
R has a multiplicative inverse (the inverse) where a(1/a) = 1
Identities
of Absolute Value
If a, b, c, and d ε R, then
|a + b| < |a| +
|b| Triangle Inequality
|a - b| >
|a| - |b| Subtraction Identity
|ab| =
|a|·|b| Multiplication Identity
if b ≠ 0, |a/b|
= |a|/|b| Division Identity
|a - b|
= |b - a|
-|a|<
a <|a|
|a|< b if and only if -b<
a <b