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Secant and Cosecant

"To graph secant and cosecant, find values of the reciprocal functions and plot them on the coordinate plane. Unlike the graphs of sine and cosine, secant and cosecant have vertical asymptotes wheneve ...

Double Angle Formulas

"The double angles sin(2theta) and cos(2theta) can be rewritten as sin(theta+theta) and cos(theta+theta). Applying the cosine and sine addition formulas, we find that sin(2theta)=2sin(theta)cos(theta ...

Domain Restrictions

"An important concept in the study of functions, especially piece-wise defined functions, is that of domain restrictions. Domain restrictions allow us to create functions defined over numbers that wor ...

Distance Formula in 3D

"There are two formulas that are important to remember when considering vectors or positions in the 3D coordinate System. The midpoint formula and the distance formula in 3D. The midpoint and distance ...

Recursion Sequences

"While arithmetic and geometric sequences involve a rule that uses a constant number, recursion sequences use the terms themselves in the rule. One term in recursion sequences is determined from using ...

Rectangular Form to Trigonometric Form

"Both the trigonometric form and the rectangular form are useful ways to describe complex numbers, and so we must understand how to convert from rectangular form to trigonometric form. To convert from ...

Reciprocal Trigonometric Functions

"There are three reciprocal trigonometric functions, making a total of six including cosine, sine, and tangent. The reciprocal cosine function is secant: sec(theta)=1/cos(theta). The reciprocal sine ...

Reciprocal Transformation

"One important concept in the study of polynomials is the reciprocal transformation. What happens when we take the reciprocal transformation of a function, or one over the function? Specifically, ther ...

Difference Quotients

"To find the slope of the secant line between two points in a function, we use difference quotients. Difference quotients are used with limits in the definition of the derivative and are important to ...

Rational Functions

"Once we have a thorough understanding of polynomials we can look at rational functions that are a quotient of two polynomials. These rational functions have certain behaviors, and students are often ...

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