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Two Column Proofs

"Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "pro ...

Invertible Square Matrix

"In order to determine if a matrix is an invertible square matrix, or a square matrix with an inverse, we can use determinants. The only matrix with a nonzero determinant is an invertible square matri ...

Trigonometric Identities

"Identities are equations true for any value of the variable. Since a right triangle drawn in the unit circle has a hypotenuse of length 1, we define the trigonometric identies x=cos(theta) and y=sin( ...

Inverse Variation

"When modeling real world situations, we often use what's called inverse variation to describe a relation between two variables. Inverse variation is a relation in which the absolute value of one vari ...

Trigonometric Form of Complex Numbers

"A convenient form for numbers in the complex plane, other than rectangular form, is the trigonometric form of complex numbers. The trigonometric form of complex numbers uses the modulus and an angle ...

Inverse Trigonometric Functions

"Once we understand the trigonometric functions sine, cosine, and tangent, we are ready to learn how to use inverse trigonometric functions to find the measure of the angle the function represents. In ...

Inverse Tangent Function

"Since tangent is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted tangent function. The graph of the inverse tangent function is a reflection of ...

Tricky Substitutions Involving Radicals

"When an indefinite integral involves a function of x times the radical of another function of x, the substitution method must be used in multiple ways. In these tricky substitutions involving radical ...

Inverse Sine Function

"Since sine is not a one-to-one function, the domain must be limited to -pi/2 to pi/2, which is called the restricted sine function. The inverse sine function is written as sin^-1(x) or arcsin(x). I ...

Inverse Cosine Function

"Since cosine is not a one-to-one function, the domain must be limited to 0 to pi, which is called the restricted cosine function. The inverse cosine function is written as cos^-1(x) or arccos(x). I ...

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