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

By | October 4, 2016

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 one side and the numeric value on the other side.

3) Locate the quadrants that make the equation true.

4) Identify the special triangle and substitute in the appropriate the values.

```30,60,90: x, x√3, 2x
45,45,90: x, x, x√2```

5) Identify the angle in question based on the quadrant and the special triangle.

Find the reference angle(s).

Convert angle(s) to radians by multiplying it by π/180.

6) Add the period of the trigonometric function times an integer, k, to represent all of the solutions.

```cosine period = 2π
sine period = 2π
tan period = π```

7) Verify your results using the Texas Instrument Graphing Calculator. TI-84, TI-84 Plus, TI-84 C

You have just found all of the solutions that make this trig equation true.