'Mathematics st stephen' diaporamas de présentation

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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Polynomial Functions

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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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Angles and

Angles and. Their Measure. An angle is formed by joining the endpoints of two half-lines called rays. . The side you measure to is called the terminal side. Angles measured counterclockwise are given a positive sign and angles measured clockwise are given a negative sign. Terminal Side.

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CIRCLES

CIRCLES. The standard form of the equation of a circle with its center at the origin is . r is the radius of the circle so if we take the square root of the right hand side, we'll know how big the radius is.

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Solving

Solving. Quadratic. Equations. A quadratic equation is an equation equivalent to one of the form Where a , b , and c are real numbers and a ? 0. So if we have an equation in x and the highest power is 2, it is quadratic.

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RATIONAL

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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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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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ARITHMETIC SEQUENCES

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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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PROGRAMMING

Linear programming techniques are used to solve a wide variety of problems, such as optimising airline scheduling and establishing telephone lines. PROGRAMMING. LINEAR.

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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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Remainder and Factor Theorems

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