# Category Archives: Algebra II – Trigonometry

## Algebra – Find the vertex of the quadratic equation

By | November 30, 2016

Find the vertex of the quadratic equation In this tutorial students learn how to find the vertex of a quadratic equation (parabola) using various methods.  Those methods include graphing with the TI 84 C, calculus, and algebra methods like completing the square. When using the calculator I could have also used the MINIMUM function. 2ND |… Read More »

## Algebra – Quadratic Equations Basics

By | November 28, 2016

Quadratic Equations Basics Basic information on quadratic equations, methods to solve them, vertices, discriminant and other characteristics.

## Matrices – Solve using Cramer’s Rule on a 3 x 3 matrix – Method II

By | November 26, 2016

Cramer’s Rule on a 3 x 3 Matrix In just over 10 minutes the students will learn and understand how to use Cramer’s Rule in a simple step-by-step approach.  In this tutorial students explore how to solve 3 x 3 matrices.  They are presented with a system of 3 linear equations.   The students will also learn how to… Read More »

## Trigonometry – Unit Circle Construction – COUNTING METHOD

By | October 6, 2016

Unit Circle Construction – COUNTING METHOD In this tutorial students learn how to create the Unit Circle based off of memorization. Virginia Standards of Learning (SOL) T.1, T.2, T.3 Notice how all of the (x,y) values have a denominator of 2. Notice the 1, 2, and 3 counting technique used for each of the numerators. Take the square… Read More »

## Trigonometry – Unit Circle construction from scratch

By | October 5, 2016

Unit Circle construction from scratch In this tutorial students learn how to create the Unit Circle based on knowledge of the 30,60,90 and 45,45,90 special triangle and fact that x=cos(theta) and y=sin(theta). Virginia Standards of Learning (SOL) T.1, T.2, T.3 Notice how all of the (x,y) values have a denominator of 2. Notice the 1, 2, and 3… Read More »

## Trigonometry – Solve Quadratic Trigonometric Equation over the Interval [0,2pi)

By | October 4, 2016

Quadratic Trigonometric Equation In this tutorial students learn how to solve a quadratic trigonometric equation over a specified interval, [0,2π). The students then verify the solutions using the GRAPH, TABLE, WINDOW and ZOOM features of the TI-84C. Virginia Standards of Learning(SOL) T.8 1) Simplify and/or factor the equation if necessary. 2) Get the trigonometric function on… Read More »

## Trigonometry – Sine Trigonometric Equation with a Horizontal Shift

By | October 3, 2016

Sine Trigonometric Equation with a Horizontal Shift In this tutorial students learn how to find all of the solutions to a trigonometric equation over a specified interval, [0,2π). The students then verify the solutions using the GRAPH, WINDOW and TRACE features of the TI-84C. Virginia Standards of Learning(SOL) T.8 1) Simplify and/or factor the equation if necessary.… Read More »

## Trigonometry – Tangent Trigonometric Equation – Find all solutions

By | October 2, 2016

Tangent Trigonometric Equation – Find all solutions In this tutorial students learn how to find all of the solutions to a trigonometric equation. The students then verify the solutions using the GRAPH, WINDOW and TRACE features of the TI-84C. Virginia Standards of Learning(SOL) T.8 1) Simplify and/or factor the equation if necessary. 2) Get the trigonometric function… Read More »

## Trigonometry – Trigonometric Identities – Example 6

By | October 1, 2016

Trigonometric Identities In this tutorial the students learn how to use trigonometric identities and properties of trigonometry to prove that trigonometric expressions are equal. Virginia Standards of Learning (SOL) T.5 Key Skills Trigonometric Identities 1/cos(x) = sec(x) 1/sin(x) = csc(x) tan(x) = sin(x)/cos(x) 1/tan(x) = cos(x)/sin(x) 1/tan(x) = cot(x) Pythagorean Identities sin²x + cos²x = 1 1… Read More »

## Trigonometry – Keys to remember the 6 Basic Trigonometric Functions

By | September 30, 2016

6 Basic Trigonometric Functions In this tutorial the students will learn about the 6 Basic Trigonometric Functions.  They will also see how the functions relate to the Unit Circle and Right Triangles.  Lastly, the students will also be introduced to the Pythagorean Identities. Key Skills Pythagorean Identities sin²x + cos²x = 1 1 + cot²x = csc²x tan²x +… Read More »