Hey, everyone. So up to this point, we've been spending a lot of time talking about trigonometric functions as well as inverse trigonometric functions. In this video, we're going to be tying these concepts together by talking about how we can use a calculator to solve problems that involve these types of functions. I will say that for certain problems, you're actually going to have to use your calculator to evaluate the function rather than just using the fraction or ratios that we learned about before. This can be pretty complicated, especially when you're not too sure how to use your calculator properly, but that's what we're gonna be going over in this video. I'm going to be walking you through the steps that you need to take to evaluate these types of trigonometric functions and solve these problems. So without further ado, let's get right into things.
For trig functions, you're going to need to use the sine, cosine, and tangent buttons on your calculator, which should look something like this. When dealing with problems where you have to evaluate the trig function on a calculator, you need to make sure you're in the correct mode. The mode button is something that should also be on your calculator. When you press the mode button, you'll be taken to a certain menu, and on this menu, you will have an option to choose between degrees or radians. Depending on which of these you choose is dependent on the type of problem that you're solving, but you need to know when to be in the correct mode for the type of problem. Let's take a look at some examples to make sure that we know how to do this.
Here we have an example which says, find the value of each of the following trigonometric operations and round to the nearest 10th. Keep in mind that the nearest 10th would be the nearest number or the first number after the decimal place. Let's start with example a, where we're asked to find the sine of 37 degrees. Notice in this example, we have a degree sign. Because we have degrees, that means we want to be in degree mode on our calculator. Once you've switched to degree mode, you're going to type in the sine, which is a button on your calculator, and then put 37 within these parentheses. Close the parentheses and then hit enter. Once you click enter on your calculator, rounded to the nearest tenth, you should get about 0.6. So 0.6 would be the decimal approximation for what you get from the sine of 37 degrees, and that's example a.
Now let's take a look at example b, where we're asked to find the tangent of \( \frac{2\pi}{15} \). Notice in this example, we're dealing with pi. Because of this, you actually want to be in radian mode for this example. Go to mode on your calculator, and switch to radians. Once you've done this, find the tangent button on your calculator, and then type in \( 2\pi \) and then divide that by 15. Close the parenthesis and press enter. Once you press enter, you should get about 0.4 rounded to the nearest tenth. So that's going to be the answer for example b.
Now let's take a look at example c, where we're asked to find the secant of 50 degrees. Notice again that we have a degree symbol here, which means we want to be in degree mode for this example. The problem with this situation is we don't have a secant button on our calculator. But if you recall from the reciprocal identities, secant is the same thing as one over cosine. This would be the same as taking 1 and dividing it by the cosine of 50 degrees. Put in 1 into your calculator, and then divide it by the cosine of 50. Close that parenthesis, and then hit enter. When you hit enter on the calculator, you should get an approximate value of 1.55, but rounded to the nearest tenth, we can say that's 1.6. So 1.6 would be the answer for example c.
Let's try example d, where we're asked to find the arctangent of three-fourths. We are asked to find our answer in degrees, so we want to be in the degree mode on our calculator. The arctangent is the same thing as the inverse tangent. Whenever you're dealing with an inverse trig function, you want to press the second button on your calculator. Once you press the second button, then press the associated trigonometric function, which should give you the inverse of that trig function. Go to your calculator, press the second button, and then once you've pressed second, press on tangent. This will give you the inverse tangent. From here, type in \( \frac{3}{4} \), close the parenthesis, and hit enter. You should get an approximate value of 36.9 degrees rounded to the nearest tenth. So 36.9 degrees is the answer for example d.
This is how you can evaluate trigonometric and inverse trigonometric functions on your calculator. I hope you found this video helpful. Thanks for watching, and let me know if you have any questions.