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Ojk World of Math: Relationships Between the Functions
This tutorial discusses relationships among all the trig identities. Examples are given on how to apply them to simplify trig expressions and prove identities.
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Ojk's Precalculus Study Page: Sample Test
A practice test on exponents and logarithms, covering the basics and going through solving exponential and logarithmic equations.
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Ojk's Precalculus Study Page: Sum and Difference Formulas for Tangent
This tutorial introduces the sum and differnce formulas for tangent, and gives several examples of problems to be solved as well as proving other identities. Assumes knowledge of the sum and difference formulas for sine and cosine.
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Ojk's Precalculus Study Page: Measurement of Angles
An introduction to radian measurement, including converting between radians and degrees. Includes several examples and lots of pictures.
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Ojk's Precalculus Study Page: Inverse Trig Functions
An introduction to the inverse trigonometric functions, concentrating on the domain restrictions, which are explained graphically. Several examples and exercises with solutions are included, as well as a quiz.
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Ojk's Precalculus Study Pages: Solving Right Triangles
An introduction to all six trigonometric function in the setting of right triangles. This tutorial begins with the six definitions and goes through applications involving angles of elevation and angles of depression. Includes several...
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Ojk's Precalculus Study Page: Area of a Triangle
An introduction to finding the area of a triangle using the sine function. Includes several pictures and examples.
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Ojk's Precalculus Study Page: Double and Half Angle Formulas
This tutorial introduces the double-angle and half-angle formulas for sine, cosine, and tangent, and gives sample application and proof exercises. Assumes knowledge of the sum and difference formulas.
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Ojk's Precalculus Study Page: Functions
An introduction to the basic terminology of functions, including how to use the vertical line test on the graph of a relation as a means of testing whether or not it is a function.
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Ojk's Precalculus Study Page: Operations on Functions
An introduction covering how to add, subtract, multiply, divide, and find the composite of functions. Includes examples and sample exercises with solutions.
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Ojk's Precalculus Study Page: Reflections and Symmetry
An introduction to the various types of symmetries that can occur in the graphs of functions. Uses vertical, horizontal, and oblique reflections as a means of recognizing symmetries.
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Ojk's Precalculus Study Page: Quadratic Functions: Graphs
A tutorial devoted to the steps used to graph a quadratic function. Includes tables, graphs, and several sample problems.
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Ojk's Precalculus Study Page: Rational Exponents
A basic introduction to rational exponents, beginning with the definition and working up to an application. Includes several examples.
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Ojk's Precalculus Study Page: Exponential Functions
An introduction to exponential functions, concentrating on models of exponential growth and decay.
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Ojk's Precalculus Study Page: Logarithmic Functions
A wonderful study tutorial explaining logarithmic functions. Learn how to solve simple logarithmic functions. Includes many graphs and examples.
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Ojk's Precalculus Study Page: The Law of Cosines
An introduction to solving acute and obtuse triangles by using the law of cosines, including a derivation of the formula. Includes several pistures and examples.
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Ojk's Precalculus Study Page: Limits of Infinite Sequences
A wonderful study tutorial explaining the limits of infinite sequences. There are theorems and examples.
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Ojk's Pre Calculus Study Page
This online tutorial explains different topics in pre-calculus. Offers helpful information to explain different concepts. Good for review.
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Ojk's Precalculus Study Page: Applications to Trig Navigation and Surveying
This tutorial applies all of the tools from triangle trigonometry to two specific cases: navigation and surveying. There are examples of each, as well as several exercises with solutions.
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Ojk's Precalculus Study Page: Sum and Difference Formulas for Sine and Cosine
An introduction to trigonometric identities, beginning with the sum and difference formulas. Some of the formulas are proven, some are left to the reader. Includes several examples and pictures.
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Ojk's Precalculus Study Page: Linear Inequalities and Absolute Value
This tutorial demonstrates how to solve linear equalities. It also defines absolute value and demonstrates how to solve problems involving absolute value.
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Ojk's Pre Calculus Study Page: The Four Other Trig Functions
Trigonometry ratios and their signs are given in this explanation of the other trig functions. Graphs of tangent, cotangent, secant, and cosecant are given. Examples are included.
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Ojk's Precalculus Study Page: The Law of Sines
An introduction to solving acute and obtuse triangles by using the law of sines, including a derivation of the formula. Includes several pictures and examples.
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Ojk's Precalculus Study Page: Remainder and Factor Theorems
An introduction to two important uses of synthetic substitution, the remainder theorem and the factor theorem. Includes examples and sample problems with solutions.