# Math Analysis – Solve Cosine Trigonometric Equation over the interval [0,2pi)

By | September 14, 2016

## Cosine Trigonometric Equation over an interval

In this tutorial the student will learn how to solve a trigonometric equation over a specified interval, [0,2pi). The students will also 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, √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 pi/180.

6) Add the period of the trig 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 trigonometric equation true.