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Parent Graphs, their equations, and transformations

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Parent Graphs, their equations, and transformations

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Amplitude Modifies the “intensity” of sine and cosine functions, and modifies the “half” point in a tangent function

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Tangent’s period is pie/B

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Standard graph of sine, cosine, secant, and cosecant have a period of 2pi and an A value of 1, while standard form of tangent and cotangent has a period of pi and an A value of 1

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Period for sine and cosine are 2pi while tangent is 1pi

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Period for sine and cosine are 2pi while tangent is 1pi

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The domain for sine and cosine graphs is always all real numbers. 

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The domain for sine and cosine graphs is always all real numbers. 

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Domain and range

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For Inverses, switch the asymptotes & zero’s (Zero’s become assymptotes, Asymptotes become Zeros)

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Y values are extrapolated from the coordinates on the Unit Circle and the X values are from the angles measured in Radians.

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Y values are extrapolated from the coordinates on the Unit Circle and the X values are from the angles measured in Radians.

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Graph the parent function first then translate, it will be easier

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In tangent domain is restricted by asymptotes

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Inverse Trig Functions

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What A,B,C, and D does to the graph

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Inverse graphs require you to graph the corresponding trig function first, and 0’s become asymptotes

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Tangent has asymptotes for the graph

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Tangent graph domains are restricted by asymptotes 

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Tangent graph domains are restricted by asymptotes 

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Usually graphed in terms of pi

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The tangent graphs include asymptotes

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Cotangent has the same period as tangent

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Reciprocal identies

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SOHCAHTOA
Sin- opposite/hypotenuse
Cos- adjacent/hypotenuse
Tan- opposite/adjacent

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Make sure when you are doing a verified question that the two end equations are identical to each other

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Substitution

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Sin^2 theta times Cos^2 theta = 1
1+tan^2 theta = sec^2 theta
cot^2 theta + 1 = csc^2 theta

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Vectors (direction and magnitude)

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Going between parametric and Cartesian

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Two dimensional motion

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Physics

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Law of Sines, Law of Cosines

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Unit circle

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Going from Cartesian and polar form

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Polar and parametric forms

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Circle, cardiod, limacon, lemniscate,  rose curve, archamedies spiral

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Circle, cardiod, limacon, lemniscate,  rose curve, archamedies spiral

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Products and quotients of numbers in polar form

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DeMoirve’s Theorum

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Complex numbers in polar form

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Área of oblique triangles

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Ambiguous case ?

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Standard form

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Positives and negatives are crucial

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All conics fit within a cone

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Foci

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Directrix

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Everything in parentheses is opposite sign

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Elipses

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Transformations (sometimes they say what they actually are and sometimes it’s the opposite of what they are)

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Vertex

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Ellipses: c^2=a^2-b^2
Hyperbolas: c^2=a^2+b^2

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How to find directrix

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X=h y=k

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If determinant is 0, there is no inverse.

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Matrix

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Det(x)/(Det) = X

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Matrices

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Inequalities

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Substitution/Elimination

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Inverse of matrix

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Creamer’s rule (idk spelling)

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Determinant of matrix

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Determinant for 2x2 & 3x3

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Eliminating opposite coeffecients