# Trigonometry – Cosine Trigonometric Equation – Find all solutions

By | September 26, 2016

## Cosine 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 on one side and the numeric value on the other side.

3) Locate the quadrants that make the equation true.

`I, II, III, IV`

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 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.