How to find all the solutions to a sine trigonometric equation

In this tutorial learn How to find all the solutions to a sine trigonometric equation. We then verify the solutions using the GRAPH, WINDOW and TRACE features of the TI-84C.

1) Simplify and/or factor the equation if necessary.

2) Get the trig 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 square root 3, 2x
45,45,90: x, x, square root 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 = 2pi
sine period = 2pi
tan period = pi

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.

[SuperMEATman]

Thank you so much, your really a game changer.

[insaneinferno]

WOW you are a life saver! This video helped me so much :)