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Vectors and Planes

"An important calculation when dealing with vectors and planes, is being able to find a vector normal to a plane through a specific point. There are methods for finding the normal or perpendicular vec ...

Vector Equation of a Line

"We can use vectors to create the vector equation of a line. In order to create the vector equation of a line we use the position vector of a point on the line and the direction vector of the line. In ...

Vector Dot Product

"An operation used frequently on vectors is the vector dot product, sometimes known as the scalar product. The vector dot product is an operation on vectors that takes two vectors and produces a scala ...

Using Trigonometric Identities

"When simplifying problems that have reciprocal trig functions, start by substituting in the identities for each. If possible, write tangent in terms of sine and cosine. Use algebra to eliminate any ...

Using the Sine and Cosine Addition Formulas to Prove Identities

":Applying the cosine addition and sine addition formulas proves the cofunction, add pi, and supplementary angle identities. Using the formulas, we see that sin(pi/2-x) = cos(x), cos(pi/2-x) = sin(x) ...

Using Sine to Calculate the Area of a Triangle

"Using the standard formula for the area of a triangle, we can derive a formula for using sine to calculate the area of a triangle. Using sine to calculate the area of a triangle means that we can fin ...

Unit Vectors

"One special type of vectors are unit vectors. Unit vectors have a magnitude of one, and the specific unit vectors i and j represent the positive horizontal and vertical unit vectors in a two dimensio ...

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( ...

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 ...

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