'Stephen corcoran head' presentation slideshows

THE UNIT CIRCLE

THE UNIT CIRCLE. A circle with center at (0, 0) and radius 1 is called a unit circle. . The equation of this circle would be . (0,1). (-1,0). (1,0). (0,-1). So points on this circle must satisfy this equation. .

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GRAPHS OF

GRAPHS OF. SINE AND COSINE FUNCTIONS. y. 1. x. - 1. We are interested in the graph of y = f ( x ) = sin x. Start with a "t" chart and let's choose values from our unit circle and find the sine values. plot these points. x y = sin x.

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Matrix Algebra

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Matrix Algebra

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Systems of Linear Equations

Systems of Linear Equations. Three Equations Containing Three Variables. The first two cases are called consistent since there are solutions. The last case is called inconsistent. The solution will be one of three cases:

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GRAPHS OF OTHER TRIG FUNCTIONS

GRAPHS OF OTHER TRIG FUNCTIONS. We are interested in the graph of y = f ( x ) = tan x. Start with a "t" chart and let's choose values from our unit circle and find the tangent values. Tangent has a period of ? so it will repeat every ?. y. would mean there is a vertical asymptote here.

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Graphing Techniques:

Graphing Techniques:. Transformations. Transformations: Review. Transformations. We will be looking at functions from our library of functions and seeing how various modifications to the functions transform them. Transformations. Transformations. Transformations. Transformations.

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INVERSE

INVERSE. FUNCTIONS. 1. 2. 2. 4. 3. 6. 4. 8. 10. 5. Remember we talked about functions---taking a set X and mapping into a Set Y. 1. 2. 2. 4. 3. 6. 4. 8. 10. 5. Set X. Set Y. An inverse function would reverse that process and map from Set Y back into Set X.

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( r , ? )

( r , ? ). We are going to look at a new coordinate system called the polar coordinate system. You are familiar with plotting with a rectangular coordinate system. The center of the graph is called the pole . Angles are measured from the positive x axis.

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VECTORS

VECTORS. A vector is a quantity that has both magnitude and direction. It is represented by an arrow. The length of the vector represents the magnitude and the arrow indicates the direction of the vector. Blue and orange vectors have same magnitude but different direction.

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RATIONAL

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PARAMETRIC

PARAMETRIC. Q. U. A. T. I. 0. N. S.

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Integration by Substitution

Integration by Substitution. The chain rule allows us to differentiate a wide variety of functions, but we are able to find antiderivatives for only a limited range of functions? We can sometimes use substitution or change of variable to rewrite functions in a form that we can integrate.

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The Binomial Theorem

The Binomial Theorem. A binomial is a polynomial with two terms such as x + a. Often we need to raise a binomial to a power. In this section we'll explore a way to do just that without lengthy multiplication. Can you see a pattern? Can you make a guess what the next one would be?.

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The Binomial Theorem

The Binomial Theorem. A binomial is a polynomial with two terms such as x + a. Often we need to raise a binomial to a power. In this section we'll explore a way to do just that without lengthy multiplication. Can you see a pattern? Can you make a guess what the next one would be?.

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Sum and Difference Formulas

Sum and Difference Formulas. Often you will have the cosine of the sum or difference of two angles. We are going to use formulas for this to express in terms of products and sums of sines and cosines. The formulas are:.

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THE DOT PRODUCT

THE DOT PRODUCT. The definition of the product of two vectors is:. 1. This is called the dot product . Notice the answer is just a number NOT a vector.

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TRIGONOMETRIC IDENTITIES

TRIGONOMETRIC IDENTITIES. Remember an identity is an equation that is true for all defined values of a variable. We are going to use the identities that we have already established to "prove" or establish other identities. Let's summarize the basic identities we have. RECIPROCAL IDENTITIES.

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Equations of Lines

Equations of Lines. Equations to Remember. Slope-Intercept Form. Useful for graphing since m is the slope and b is the y-intercept. Point-Slope Form. Use this form when you know a point on the line and the slope

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Separable Differential Equations

Separable Differential Equations. Separable Differential Equations. A separable differential equation can be expressed as the product of a function of x and a function of y. Example:.

1.72k views • 6 slides