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Trigonometric Identities and Equations

Simplifying Trigonometric Expressions When Simplifying Trigonometric Identities it is important not to get frustrated and give up. The purpose of simplifying Trigonometric Identities is to simplify the expression to one single trigonometric function or number. To do this it is often helpful to follow a step by step process. While following these steps may ...

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PC 4.4 Graphing Sine and Cosine with Transformations

In this unit I will show you how to graph the sine and cosine function when given different transformations such as amplitude, period change, phase shift as well as vertical transformations. Graphing Sine with a change in Amplitude Graphing Sine with a change in Period Graphing Sine with a phase shift Graphing Sine with ...

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PC 4.3 Circular Trigonometric Functions

In this unit we will look at evaluating the six trigonometric functions by creating a triangle based on a point, trigonometric equation with a constraint as well as using the Unit circle. Evaluating the six trigonometric functions given a point Evaluating the six trigonometric functions given an trigonometric equation and constraint ex 1 Evaluating ...

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Pc 4.2 Trigonometric Functions with Triangles

In this video post we will explore how to evaluate the six trigonometric functions given a triangle as well as given a trigonometric equation that we use to create a triangle so that we can evaluate. Evaluate the six trigonometric functions given a triangle Evaluate the six trigonometric functions given a trigonometric equation ...

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Pc 4.1 Angles and Their measures

Angles and their measures Most of us understand angles from Geometry.  However we only discussed angle measure in degree form. In this section we will explore angles and their measures in Radians and Degree-Minutes-Seconds or DMS form.  These are equivalent ways to measure angles and we will use all three in later chapters so ...

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ALg2 Complex Numbers

Exiting out of the real number system we enter the the imaginary number system.  Imaginary numbers are categorized by their use of the imaginary unit i which is represented by the root of -1.  When imaginary numbers are combined with real numbers we call them complex numbers.  In this post we will explore operations ...

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ALG2 Unit 3 – Solving Quadratic Equations

Solving quadratic equations is different than solving linear equations.  When solving linear equations we are looking for the value of x that makes the equation true.  When solving quadratic equations we are looking for the values of x that make the equation equal to zero.  If we explore a quadratic we notice that the ...

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PC 2.6/2.7 Graphing and Solving Rational Functions

In these two sections we will explore rational functions.  Rational functions are not polynomials but actually the quotient of two polynomials.  In the formal definition we define a rational functions as R(x)=N(x)/D(x).  This understanding will be very helpful when identifying the vertical and horizontal asymptotes while graphing rational functions.  There are other pieces of ...

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Pc 2.3/2.4 Real and Complex Zeros of Polynomials

To understand zeros of polynomials it is important to understand where they come from.  We can quickly find the zeros of a polynomial when we know the factors.  When a polynomial is in factored form we can use the zero product property to find the zeros.  However it is also important to understand that ...

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