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. And 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. Now, something that I will say is 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. Now, this can be pretty complicated, especially when you're not too sure how to use your calculator properly, but that's what we're going to be going over in this video. And 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. Now, 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. Now, 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. Now, the mode button is something that should also be on your calculator. And 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. Now, 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. So, let's actually take a look at some examples to make sure that we know how to do this. So here we have an example which says, find the value of each of the following trigonometric operations and round to the nearest 10th. And keep in mind that the nearest 10th would be the nearest number or the first number after the decimal place. Now, let's start with example a, where we're asked to find the sine of 37 degrees. Now, notice in this example, we have a degree sign. And because we have degrees, that means that we want to be in degree mode on our calculator. So, once you've switched to degree mode, you're going to type in the sign, which is a button on your calculator. And then what you're going to do is put 37 within these parentheses. You're going to close the parentheses and then hit enter. Once you click enter on your calculator, round it 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. But now let's take a look at example b, where we're asked to find the tangent of 2 pi over 15. Now, notice in this example, we're dealing with pi. And because of this means you actually want to be in radian mode for this example. So, go to mode on your calculator, and switch to radians. Once you've done this, you're going to find the tangent button on your calculator, and then you're going to type in \( 2 \pi \) and then divide that by 15. You're then going to 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. Now I again notice that we have a degree symbol here, which means we want to be in degree mode for this example. Now, the problem with this situation is we don't really have a secant button on our calculator. But if you recall from the reciprocal identities, secant is the same thing as one over cosine. So this would be the same thing as taking 1 and dividing it by the cosine of 50 degrees. So, what I'm going to do is put in 1 into my calculator, and then divide it by the cosine of 50. You can then close that parenthesis, and then you could hit enter. And 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 that's 1.6. So 1.6 would be the answer for example c. Now let's try example d, where we're asked to find the arctangent of 3 fourths. Now, we are asked to find our answer in degrees, so we want to be in degree mode on our calculator. But the question becomes how can we find the arctangent of something? Well, we actually discussed this in previous videos. The arctangent is the same thing as the inverse tangent. And whenever you're dealing with an inverse trig function, what you wanna do is you want to press the second button on your calculator. This is a button that you should see. Once you press the second button, you're then going to press the associated trigonometric function, and this should give you the inverse of that trig function. So what you wanna do is go to your calculator, and you wanna press the second button. And then once you've pressed second, you're going to press on tangent. This will give you the inverse tangent. And from here, you can type in 3 divided by 4, and then close the parenthesis. Once you've done this, you can hit enter on this, and 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. So this is how you can evaluate trigonometric and inverse trigonometric functions on your calculator. So, hope you found this video helpful. Thanks for watching, and let me know if you have any questions.
Table of contents
- 0. Fundamental Concepts of Algebra3h 29m
- 1. Equations and Inequalities3h 27m
- 2. Graphs1h 43m
- 3. Functions & Graphs2h 17m
- 4. Polynomial Functions1h 54m
- 5. Rational Functions1h 23m
- 6. Exponential and Logarithmic Functions2h 28m
- 7. Measuring Angles39m
- 8. Trigonometric Functions on Right Triangles2h 5m
- 9. Unit Circle1h 19m
- 10. Graphing Trigonometric Functions1h 19m
- 11. Inverse Trigonometric Functions and Basic Trig Equations1h 41m
- 12. Trigonometric Identities 2h 34m
- 13. Non-Right Triangles1h 38m
- 14. Vectors2h 25m
- 15. Polar Equations2h 5m
- 16. Parametric Equations1h 6m
- 17. Graphing Complex Numbers1h 7m
- 18. Systems of Equations and Matrices1h 6m
- 19. Conic Sections2h 36m
- 20. Sequences, Series & Induction1h 15m
- 21. Combinatorics and Probability1h 45m
- 22. Limits & Continuity1h 49m
- 23. Intro to Derivatives & Area Under the Curve2h 9m
8. Trigonometric Functions on Right Triangles
Trigonometric Functions on Right Triangles
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