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CLEP Precalculus: Study Guide & Test Prep9 chapters | 75 lessons | 18 flashcard sets

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Lesson Transcript

Instructor:
*Heather Higinbotham*

In this lesson, review how to use the history on the CLEP calculator as we calculate sines, cosines and the inverse trigonometric functions. Finish by exploring exponentials and logarithms.

Let's take another look at the CLEP calculator. In particular, let's take a look at the history in a CLEP calculator, as well as various functions that you can use on a CLEP calculator.

First, let's say that you type in a couple of commands, say 7 / 9, and you click 'Enter'. And then, you type in the command 2 + 9, 'Enter'. Both of these are going to be shown in your history. So, if I click on the 'H' with the blue circle around it, I see 7 / 9, which gave me .7777777 and 2 + 9, which gave me 11, so I can see all of the previous entries that I had in here.

Let's say I need to solve the equation cos*x* = 1/3 using a calculator. Now I know that I could take the inverse cosine of both sides of this function and end up with *x* equals the inverse cosine of 1/3. This inverse cosine is also known as the arccosine, and on the CLEP calculator it's listed as 'ACOS', so arccosine. Let's find the arccosine of 1/3. Arccos(1/3) = 1.23, but that's in radians. Let's say I'm looking for arccosine of 1/3 in degrees. That gives me 70.5 degrees, so cos(70.5 degrees) = 1/3.

Now let's use the exponential function. That is *e*. So, let's say *e* to the 1 gives me the value of *e*. That's *e* to the 1st power. Here this little caret, ^, means *raised to*, so *e*^1 is exactly like *e* superscript 1. So that gives me the value of *e*, which is 2.7. Log, 'log', and natural log, denoted *ln*, are the inverse functions of these. Remember that if you write *e*^*x*=*y* the inverse is the natural log. So if you take the natural log of this equation, then ln*y*=*x*. Similarly, with 10, you have 10^*x*=*y*, then log*y*=*x*.

What if you have something that is different from *e* or 10, let's say 3. Say you have 3^*x*=9. The inverse of this is log base 3. So, in this case, log base 3 of 9 will give you *x*, but how do you write log base 3 of 9 on a calculator? Well, you need to use the base formula. That is log(9) / log(3) is the same thing as the log base 3 of 9. So let's do that on the CLEP calculator. Take the log(9) / log(3). This gives me 2, which is exactly what I would expect, because 3^2=9. Let's show explicitly that *e*^*x* and the natural log are inverse functions. So, let's find *e*^4. *e*^4=54.6. Now if the natural log is the inverse of this function, I can take the natural log of 54 and get back 4. So *e*^4=54.

So let's review a couple of hints that we learned in this lesson. First, you can click on the history to view all of the previous results of your calculations. If you click on one of these results, say you click on 'H16', that will insert the result from that 16th calculation into your current calculation. Finally, when dealing with functions, keep in mind that the caret equals superscript. So, *e*^2 is the same as saying *e* squared. If you want to calculate the log base 2 of 4, you need to write log(4) / log(2). Finally, if you want to calculate the inverse trigonometric functions, first remember to keep in mind if you are using radians or degrees; second, the inverse trigonometric functions are given as arccosine and arcsine.

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CLEP Precalculus: Study Guide & Test Prep9 chapters | 75 lessons | 18 flashcard sets

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