#### Study sets matching "alg ii trig honors"

#### Study sets matching "alg ii trig honors"

Amplitude

Arc length

Binomial Theorem

Cosine

Is half the difference between the maximum and minimum values…

The arc length is the measure of the distance along the curve…

The binomial theorem states that for every positive integer n…

In a right triangle, the ratio of the side adjacent a given a…

Amplitude

Is half the difference between the maximum and minimum values…

Arc length

The arc length is the measure of the distance along the curve…

Derivation for Pythagorean Identity

Reciprocal Identities

Tangent and Cotangent Ratio Identities

Pythagorean Identities

x^2 + y^2 = r^2 <--- Pythagorean Theorem... x^2/r^2 + y^2/r^2 <-…

cscθ = 1/sinθ... secθ = 1/cosθ... cotθ = 1/tanθ

tanθ = sinθ/cosθ... cotθ = cosθ/sinθ

cos^2θ + sin^2θ = 1... 1 + tan^2 θ= sec^2θ... cot^2θ + 1 = csc^2θ

Derivation for Pythagorean Identity

x^2 + y^2 = r^2 <--- Pythagorean Theorem... x^2/r^2 + y^2/r^2 <-…

Reciprocal Identities

cscθ = 1/sinθ... secθ = 1/cosθ... cotθ = 1/tanθ

Periodic Functions

Period

Periodic Graphs

Amplitude

Functions that repeat exactly in regular intervals called cyc…

The length of a cycle

Patterns in a graph that repeat

The amplitude of sine and cosine is half the difference betwe…

Periodic Functions

Functions that repeat exactly in regular intervals called cyc…

Period

The length of a cycle

Double- angle identities:

Half -Angle identities:

Signs of X and ... Y depend on the quadra…

The 3 double angle identities of Cos 2…

Can be used to prove trigonometric identities and can be deri…

Are useful in calculating exact values for trig expressions.

Sine Cos ... Q1 + +... Q2 + -... Q3 - -... Q4 - +

Cos(squared)theta- Sin(squared)theta. ... 2Cos(squared)theta-1…

Double- angle identities:

Can be used to prove trigonometric identities and can be deri…

Half -Angle identities:

Are useful in calculating exact values for trig expressions.

What is matrix multiplication and sum…

Rotation matrix =

sin(A + B)=

cos(A + B)=

To find the coordinates of points rotated about the origin on…

a matrix which moves a body as a rigid unit without altering…

sin A cos B + cos A sin B

cos A cos B - sin A sin B

What is matrix multiplication and sum…

To find the coordinates of points rotated about the origin on…

Rotation matrix =

a matrix which moves a body as a rigid unit without altering…

Recursive Sequences

Arithmetic Sequence

Recursive Formula

Geometric Sequence

Is a process in which each step of a pattern is dependent on…

A sequence in which each term is equal to the previous term p…

A starting value AND a recursive rule for generating a sequen…

A sequence in which each term is equal to the previous term m…

Recursive Sequences

Is a process in which each step of a pattern is dependent on…

Arithmetic Sequence

A sequence in which each term is equal to the previous term p…

Unlike trigonometric identities, most…

To solve trigonometric... equations, use…

Some trigonometric equations can be so…

If the equation is in quadratic form b…

solutions

algebraic equations

quadratic equations

quadratic formula

Unlike trigonometric identities, most…

solutions

To solve trigonometric... equations, use…

algebraic equations

complex numbers

discriminant

exponential decay

axis of symmetry

numbers written in the form a+bi where a and b are real numbe…

In the quadratic formula, b^2 - 4ac is the discriminant. The…

The graph of an exponential function with a base greater than…

A line across which a figure is "flipped" to create a reflect…

complex numbers

numbers written in the form a+bi where a and b are real numbe…

discriminant

In the quadratic formula, b^2 - 4ac is the discriminant. The…

equation of parallel/perpendicular to…

consistent and independent

consistent and dependent

inconsistent

y=mx+b; fill in for points/slope/ if given 'perpendicular to'…

exactly one solution

infinite # of solutions

no solution

equation of parallel/perpendicular to…

y=mx+b; fill in for points/slope/ if given 'perpendicular to'…

consistent and independent

exactly one solution

function

dependent variable

independent variable

domain

a relation in which each value of the independent variable ta…

The variable appearing second in the ordered pair (on the y a…

the variable appearing first in the ordered pair (on the x ax…

the set of permissible values of the independent variable (th…

function

a relation in which each value of the independent variable ta…

dependent variable

The variable appearing second in the ordered pair (on the y a…

Arithmetic Recursive formula

Geometric Recursive formula

Summing the first "n" terms of an arit…

If the summation converges then

An = (An - 1) + d

An = (An - 1) * r

S = (A1 + An) ... --------- * n... 2

The absolute value of R is less than 1 , so ... S = A1 ... -----…

Arithmetic Recursive formula

An = (An - 1) + d

Geometric Recursive formula

An = (An - 1) * r

Double- angle identities:

Half -Angle identities:

Signs of X and ... Y depend on the quadra…

The 3 double angle identities of Cos 2…

Can be used to prove trigonometric identities and can be deri…

Are useful in calculating exact values for trig expressions.

Sine Cos ... Q1 + +... Q2 + -... Q3 - -... Q4 - +

Cos(squared)theta- Sin(squared)theta. ... 2Cos(squared)theta-1…

Double- angle identities:

Can be used to prove trigonometric identities and can be deri…

Half -Angle identities:

Are useful in calculating exact values for trig expressions.

What is matrix multiplication and sum…

Rotation matrix =

sin(A + B)=

cos(A + B)=

To find the coordinates of points rotated about the origin on…

a matrix which moves a body as a rigid unit without altering…

sin A cos B + cos A sin B

cos A cos B - sin A sin B

What is matrix multiplication and sum…

To find the coordinates of points rotated about the origin on…

Rotation matrix =

a matrix which moves a body as a rigid unit without altering…

Derivation for Pythagorean Identity

Reciprocal Identities

Tangent and Cotangent Ratio Identities

Pythagorean Identities

x^2 + y^2 = r^2 <--- Pythagorean Theorem... x^2/r^2 + y^2/r^2 <-…

cscθ = 1/sinθ... secθ = 1/cosθ... cotθ = 1/tanθ

tanθ = sinθ/cosθ... cotθ = cosθ/sinθ

cos^2θ + sin^2θ = 1... 1 + tan^2 θ= sec^2θ... cot^2θ + 1 = csc^2θ

Derivation for Pythagorean Identity

x^2 + y^2 = r^2 <--- Pythagorean Theorem... x^2/r^2 + y^2/r^2 <-…

Reciprocal Identities

cscθ = 1/sinθ... secθ = 1/cosθ... cotθ = 1/tanθ

Periodic Functions

Period

Periodic Graphs

Amplitude

Functions that repeat exactly in regular intervals called cyc…

The length of a cycle

Patterns in a graph that repeat

The amplitude of sine and cosine is half the difference betwe…

Periodic Functions

Functions that repeat exactly in regular intervals called cyc…

Period

The length of a cycle

Unlike trigonometric identities, most…

To solve trigonometric... equations, use…

Some trigonometric equations can be so…

If the equation is in quadratic form b…

solutions

algebraic equations

quadratic equations

quadratic formula

Unlike trigonometric identities, most…

solutions

To solve trigonometric... equations, use…

algebraic equations

amplitude

assymtote

branches

common logarithm

for a single sine or cosine function it is half of the differ…

a line that a graph approaches more and more closely but neve…

two symmetrical parts of a hyperbola (hyperbola= graph of rat…

logarithm with a base of 10

amplitude

for a single sine or cosine function it is half of the differ…

assymtote

a line that a graph approaches more and more closely but neve…

End behavior for odd exponents

End behavior for even exponents

slope-intercept form

point slope form

Pos: down up... neg: up down

pos: up up... neg: down down

y = mx + b

y - y1 = m(x-x1)

End behavior for odd exponents

Pos: down up... neg: up down

End behavior for even exponents

pos: up up... neg: down down

Reciprocal Identities

Tangent & Cotangent Ratio Identities

Pythagorean Identities

Negative-Angle Identities

tan θ = sin θ/cos θ... cot θ = cos θ/sin θ

sin (-θ) = -sin θ... cos (-θ) = cos θ... tan (-θ) = -tan θ

Reciprocal Identities

Tangent & Cotangent Ratio Identities

tan θ = sin θ/cos θ... cot θ = cos θ/sin θ

Circle

Parabola

Ellipse

Hyperbola

The set of all points on a plane that are equidistant from a…

The set of all points in a plane that are equidistant from a…

The set of all points in plane such that the sum of the dista…

The set of all points in a plane such that the difference of…

Circle

The set of all points on a plane that are equidistant from a…

Parabola

The set of all points in a plane that are equidistant from a…

Relation

Domain

Range

Function

Set of ordered pairs

Set containing the first elements, aka x values or the input

Set containing the second elements, aka y values or the output

Relation where each member of the domain corresponds to one a…

Relation

Set of ordered pairs

Domain

Set containing the first elements, aka x values or the input

Nth term of an arithmetic sequence

Sum of 1st n terms, arithmetic series

Nth term of geometric sequence

Sum of geometric series

.... :an=a1+(n-1) d

Sn=n (a1+an/2)

:an=a1×r^n-1

Sn=a1 (1-r^n/1-r)

Nth term of an arithmetic sequence

.... :an=a1+(n-1) d

Sum of 1st n terms, arithmetic series

Sn=n (a1+an/2)

How do you determine whether a given p…

What makes a point a solution to a sys…

What does it mean if two systems are s…

A system of equations...

Plug the solution into BOTH

The solution to a system of equations are the (x,y) pairs tha…

They have the same solutions

Consists of 2 or more equations

How do you determine whether a given p…

Plug the solution into BOTH

What makes a point a solution to a sys…

The solution to a system of equations are the (x,y) pairs tha…

Formula for 45/45/90

Formula for 30/60/90 in order to find…

Formula for 30/60/90 in order to find…

Formula for sin Law

Leg times Sqrt 2 = Hypotenuse

Short leg times 2 = Hypotenuse

Short leg times Sqrt 3 = long leg

a/sin A = b/sin B = c/sin C

Formula for 45/45/90

Leg times Sqrt 2 = Hypotenuse

Formula for 30/60/90 in order to find…

Short leg times 2 = Hypotenuse

If n is odd and a is positive, x -> in…

If n is odd and a is positive, x -> -…

If n is odd and a is negative, x -> in…

If n is odd and a is negative, x -> -…

y -> inf

y -> - inf

y -> - inf

y -> inf

If n is odd and a is positive, x -> in…

y -> inf

If n is odd and a is positive, x -> -…

y -> - inf