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Understanding Pythagorean identities

PC30.1

Angle in standard position

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Coterminal angles

Coterminal Angles

Reference angle

Converting between degrees and radians

Trigonometric ratios of angles in radians

Radian measure and arc length

PC30.10

Descartes' rule of signs

Descartes' Rule of Signs

Descartes" rule of signs

Polynomial long division

Polynomial synthetic division

Polynomial functions

Recognizing a Polynomial Function

Remainder theorem

Finding the Remainder Using Synthetic Division and the Remainder Theorem

Factor theorem

Using the Factor Theorem to Test For Factors of a Polynomial

Rational zero theorem

Rational Zero Theorem

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Multiplicities of polynomials

Imaginary zeros of polynomials

Solving polynomial inequalities

Fundamental theorem of algebra

PC30.11

Radical functions and transformations

Square root of a function

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

What is a rational function?

Point of discontinuity

Slant asymptote

Determining the Equation of a Slant Asymptote Using Long Division

Determining the Equation of a Slant Asymptote Using Synthetic Division

Solving rational equations

Solving rational inequalities

Solving Rational Inequalities With Two Fractions

Basic radical functions

Basic Radical Function

Basic Radical Functions

Vertical asymptote

Horizontal asymptote

Horizontal Asymptote

Graphs of rational functions

PC30.12

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Factorial notation

Path counting problems

Permutations

Combinations

Problems involving both permutations and combinations

Permutation vs. Combination

PC30.13

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

PC30.2

Unit circle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

PC30.3

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

PC30.4

Solving first degree trigonometric equations

Solving second degree trigonometric equations

Solving trigonometric equations involving multiple angles

Solving trigonometric equations using pythagorean identities

Solving trigonometric equations using Pythagorean identities

Solving trigonometric equations using sum and difference identities

Solving trigonometric equations using double-angle identities

PC30.5

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Determining non-permissible values for trig expressions

Cofunction identities

PC30.6

Function notation (advanced)

Composite functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Operations with functions

Inequalities of combined functions

Inequalities of Combined Functions

PC30.7

Combining transformations of functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Even and odd functions

PC30.8

One to one functions

Finding inverse trigonometric function from its graph

Evaluating inverse trigonometric functions

Finding inverse reciprocal trigonometric function from its graph

Inverse reciprocal trigonometric function: finding the exact value

Inverse Reciprocal Trigonometric Function: Finding the Exact Value

Inverse functions

Difference quotient: applications of functions

PC30.9

Solving logarithmic equations

Graphing exponential functions

Graphing transformations of exponential functions

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from exponential form to logarithmic form

Product rule of logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Graphing logarithmic functions

Finding a logarithmic function given its graph

Solving exponential equations using exponent rules

Pre-Calculus 30

Angles and Trigonometric Functions

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Ex. 1:

Proving all three Pythagorean identities using the unit circle

Ex. 2:

Ex. 3

Simplifying secant squared minus one times cotangent squared

Proving sinx/(1+cosx) + sinx/(1-cosx) = 2cscx

Simplifying a trig expression using conjugates and Pythagorean identities

Proving tanx(cscx+1) equals cotx/(cscx-1) using conjugates

Pythagorean identities are formulas, derived from Pythagorean Theorem, that allow us to find out where a point is on the unit circle. Learn the tricks and tips on how to use the unit circle to derive and prove the Pythagorean identities can be difficult. 

Use sine ratio to calculate angles and sides (Sin = \(  \frac{o}{h}\) )

Use cosine ratio to calculate angles and sides (Cos =  \(  \frac{a}{h}\)  )

Factoring difference of squares: x^2 - y^2