Tips on Using a Calculator for Trigonometry

Video Transcript

"I'd like to show you a couple of things that you should remember whenever you're trying to use your calculator to do some trigonometry. One of the most important thing to remember when doing trigonometry with a calculator is to make sure that your calculator is in the correct mode. Meaning, it should be in either degrees, radians, or some other measurement whenever you're dealing with your angles. So notice that this calculator is given in degrees. To change it, you have the DRG button which changes from degrees to radians and in this case it goes to gradients. Once you ensure that your calculator is in the correct mode with respect to the units, the degrees, radiants, or gradients doing most of the trigonometry is a fairly simple task. So for instance, if I wanted to calculate the sign of 37 degrees, I would first make sure that my calculator is in degree mode, type in 37, and then hit the sign button. For in the inverse sine the domain is from -1 to 1 and the range is from negative pie over two to pie over two. For the inverse cosine the domain is negative 1 to 1 and the range is from zero to pie. For the inverse tangent, the domain is from negative infinity to infinity and the range is from negative pie over two to pie over two. If you come across a problem which says what is the inverse cosine of the square root of five over two. Well, if we try that with our calculator we would type in five to the .5 power which is the square root of five.Divide that by two and then we would do the inverse cosine. Notice that we get an error.That is because the square root of 5 is bigger than one and is not included in the domain of inverse cosine. Another problem that we could actually get some answers for is if we're asked to find all the angles such that the cosine of the angle is the square root of 3/2. So, in order to do that first we would type in the square root of 3/2. So three to the .5 power divided by two and then we'd do inverse cosine. That would give us 30 degrees. Now on the onset, one would think that that is the only angle that would give you a cosine of square root of 3/2 however there is another angle. However there is another angle. Remember that the right ang of inverse cosine is from zero to pie. So that is the only angle that you'll get from your calculator, that being 30 degrees. However another angle with the same cosine is negative 30 degrees. The 30 degrees given by your calculator is what we may call a reference angle."