The day has finally arrived! The apple powers that be have finally gave the green light. I am very excited to unveil the new pwn mathematics: sohcahtoa app for all my iTunes/iPhone listeners. I feel that this app has everything I'd look for in a sohcahtoa training tool. Allow me to take you for a walk through the various features of the app, and allow it to serve as a door-closing wrap up for the sohcahtoa topic that we've spent so much time (and episodes) covering.
The first stop on the sohcahtoa tour is the answer to the question: what is sohcahtoa? Sohcahtoa is a mnemonic device that helps you to remember the relationship between trigonometric functions of angles and the ratio of sides of a right triangle. Each letter either represents sin/cos/tan, or the sides adj/opp/hyp. There are three sections soh/cah/toa which all follow the same pattern: trig function = side/side. Example: soh represents sin = opp/hyp. If you're brand new, try to do the same for cah and toa.
Next, we need to understand which sides represent which on a right triangle. The hypotenuse is always the side which does not form the right angle on the triangle. It looks like the diagonal of a rectangle or square. The opposite and adjacent sides vary depending on which angle you are interested in. The adjacent side is always the side which forms the angle along with the hypotenuse. The opposite side is always "the other side", aka as the only side which does not form the angle of interest. As the angle of interest changes, the opposite and adjacent sides will switch.
Equipped with this information, we can now outline 6 steps to quickly and efficiently solve any problem where sohcahtoa can be applied:
1) Identify the right angle in your triangle. This confirms that you will be able to use the sohcahtoa rule.
2) Identify your angle of interest. This will change which sides are opposite and adjacent.
3) Identify your opposite and adjacent legs of the triangle.
4) Using the sohcahtoa rule, set up a relationship using sin/cos/tan, the angle, and two of the adjacent/opposite/hypotenuse sides.
5) Solve the equation for your desired variable.
6) Box your answer, you're done!
The best way to understand these steps is to put them in action. I encourage you to check out Episode 35, Episode 36, and Episode 37 where we roll through these examples in great detail.
To me, the best way to reinforce concepts is to do flash cards. Included in the app is a flash card section which rolls through the sohcahtoa ratios, as well as adjacent, opposite, and hypotenuse identification. Coming up next is vectors and component calculation where we will see the sohcahtoa application as a practical application. You will use this a zillion times in first year physics courses, so brush up and make sure you can do it in your sleep! The app is designed to be a quick review for test time, as well as a review tool to keep yourself in the zone at various points of convenient downtime, like a bus ride or waiting in line. Always use times like these to do some review. It will help your fluency immeasurably.
