Shared Flashcard Set

Details

Trig
Reciprocal functions, Quotient identities, Pythagorean identities, Even/odd, Sum and Difference Formulas, Double and Half Angle Formulas, Cofunctions, Law of Sines & Cosines, Area of Triangle
51
Mathematics
11th Grade
11/30/2011
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Cards

Term

Reciprocal Function:

 

cscθ

 Definition

   1   

sinθ
Term

Reciprocal Function

 

secθ

 Definition

   1   

cosθ
Term

Reciprocal Function

 

cotθ

 Definition

   1   

tanθ
Term

Reciprocal Function

 

sinθ

 Definition

   1   

cscθ
Term

Reciprocal Function

 

cosθ

 Definition

   1   

secθ
Term

Reciprocal Function

 

tanθ

 Definition

   1   

cotθ
Term

Quotient Identities

 

tanθ

 Definition

sinθ

cosθ
Term

Quotient Identities

 

cotθ

 Definition

cosθ

sinθ
Term

Pythagorean Identities

 

sin2θ + cos2θ

 Definition
1
Term

Pythagorean Identities

 

tan2θ + 1

 Definition
sec2θ
Term

Pythagorean Identities

 

cot2θ + 1

 Definition
csc2θ
Term

Pythagorean Identities

 

cos2θ

 Definition
1 - sin2θ
Term

Pythagorean Identities

 

sin2θ

 Definition
1 - cos2θ
Term

Even/Odd

 

cos(-θ)

 Definition
cos(θ)
Term

Even/Odd

 

sec(-θ)

 Definition
sec(θ)
Term

Even/Odd

 

sin(-θ)

 Definition
-sin(θ)
Term

Even/Odd

 

csc(-θ)

 Definition
-csc(θ)
Term

Even/Odd

 

tan(-θ)

 Definition
-tan(θ)
Term

Even/Odd

 

cot(-θ)

 Definition
-cot(θ)
Term

Sum and Difference Formulas

 

sin(α + β)

 Definition
sinαcosβ + cosαsinβ
Term

Sum and Difference Formulas

 

sin(α - β)

 Definition
sinαcosβ - cosαsinβ
Term

Sum and Difference Formulas

 

cos(α + β)

 Definition
cosαcosβ - sinαsinβ
Term

Sum and Difference Formulas

 

cos(α - β)

 Definition
cosαcosβ + sinαsinβ
Term

Sum and Difference Formulas

 

tan(α + β)

 Definition

tanα + tanβ

1 - tanαtanβ
Term

Sum and Difference Formulas

 

tan(α - β)

 Definition

tanα - tanβ

1 + tanαtanβ
Term

Double and Half Angle Formulas

  

sin(2θ)

 Definition
2sinθcosθ
Term

Double and Half Angle Formulas

  

cos(2θ)

 

In terms of sin and cos

 Definition
cos2θ - sin2θ
Term

Double and Half Angle Formulas

 

cos(2θ)

 

In terms of sin 

 Definition
1 - 2sin2θ
Term

Double and Half Angle Formulas

 

cos(2θ)

 

In terms of cos

 Definition
2cos2θ - 1
Term

Double and Half Angle Formulas

 

tan(2θ)

 Definition

2tanθ

1 - tan2θ
Term

Double and Half Angle Formulas

 

sin(θ/2)

 Definition
±√((1-cosθ)/(2))
Term

Double and Half Angle Formulas

 

cos(θ/2)

 Definition
±√((1 + cosθ)/(2))
Term

Double and Half Angle Formulas

 

tan(θ/2)

 

Method 1

 Definition

1 - cosθ

sinθ
Term

Double and Half Angle Formulas

 

tan(θ/2)

 

Method 2

 Definition

sinθ

1 - cosθ
Term

Cofunctions

 

sin(90 - θ)

 Definition
cos(θ)
Term

Cofuntions

 

cos(90 - θ)

 Definition
sin(θ)
Term

Cofunctions

 

csc(90 - θ)

 Definition
sec(θ)
Term

Cofunctions

 

sec(90 - θ)

 Definition
csc(θ)
Term

Cofunctions

 

tan(90 - θ)

 Definition
cot(θ)
Term

Cofunctions

 

cot(90 - θ)

 Definition
tan(θ)
Term
Law of Sines
 Definition

   a       b       c   

sinA   sinB   sinC
Term

Law of Cosines

 

a

 Definition

 √(b2 + c2 - 2bccosA)
Term

Law of Cosines

 

b

 Definition

 √(a2 + c2 - 2accosB)
Term

Law of Cosines

 

c

 Definition

 

 √(a2 + b2 - 2abcosC)

 
Term

Law of Cosines

 

measure of angle A

 Definition
cos-1((-a2 + b2 + c2)/(2bc))
Term

Law of Cosines

 

measure of angle B

 Definition

cos-1((a2 - b2 + c2)/(2ac))
Term

Law of Cosines

 

measure of angle C

 Definition

cos-1((a2 + b2 - c2)/(2ab))
Term

Area of Triangle

 

side a, angle C, side b

 Definition
(1/2) a b sinC
Term

Area of Triangle

 

side a, angle B, side c

 Definition

(1/2) a c sinB
Term

Area of Triangle

 

side b, angle A, side c

 Definition

(1/2) b c sinA
Term
Heron's Formula
 Definition

√(s(s-a)(s-b)(s-c))

 

s = perimeter / 2
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