Trigonometry

Trigonometry

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Hi everyone! Welcome to our own webpage. This website is created by me with the help of Mrs van den Berg to teach you trigonometry. Next to our normal classes, you can use this website to practice your skills. It's also obligatory to make the tests on the website. This shows us if you understand what we're doing en gives you instant feedback on the progress you make.

 

1. This website acts as an extra source of information. There will be lots of exercises to practice your skills.

2. You can choose your own path on this website. If you feel like things are going to slow, then feel free to scroll down to the more challenging subjects. If you feel like things are going to fast, then slow down a bit.

3. Never hesitate to ask something.

4. Do the tests on this website! It gives us insight about your development and it gives you feedback on how you are doing.

5. If you feel like something is missing... Please tell me

 

 

Planner for this chapter

Chapter 6: Trigonometry

What is trigonometry?

Trigonon means triangle in Greek

Metron means measure in Greek

 

Trigonometry is all about triangles. It helps us find the angles and lenghts of sides in triangles. Mankind has been working with trigonometry for thousands of years now. We have evidence that the Egyptians and Babylonians started calculating angles and lengths in triangles and we are still using it today in school. It's also used a lot in science and engineering, but also in sports and gaming.

 

In this chapter we're going to learn the basics of trigonometry. In year 2 you learned how to calculate the length of one side of a right-angled triangle using Pythagoras' theorem. You will recap this in the refresh exercises.

If you're interested in learning more about the history of trigonometry you can go to the EXTRA: In depth tab on this website.

6.1 Angle of elevation and tangent

In this paragraph we learn how to use the ratio height:distance to calculate the angle of elevation. The result of the division is called the gradient or tangent of ∠A. This is written as tan ∠A.

 

The book doesn't teach you the angle of depression, but it is still something you need to learn. The picture below shows you the difference between the two. If the object is higher than the angle, it is called the angle of elevation. If the object is lower than the angle, it is called the angle of depression

 

 

 

Like we said before, the result of the division is called the gradient or tangent of ∠A. This is written as tan ∠A.

Remember to always make a sketch and write down the information that you have!

 

The picture below will give you a different explanation for calculating the angle of elevation or depression which can be insightful for those who need it.

6.2 Calculating with the tangent

With trigonometry we often need to write down which sides we are calculating or which sides we already have information of. There are names to the sides that help you calculate the angles or the length of the sides. The picture below shows you what we call these sides. The hypotenuse is always the longest side. Which side is adjacent or opposite depends on the angle you are using. 

 

Use the picture above for the following questions.

 

In paragraph 6.1 they explain how you can calculate the tangent of ∠A with the length of the opposite side and the length of the adjacent side. 

In paragraph 6.2 we learn that with the tangent of ∠A and either the length of the opposite side or the adjacent side, we can calculate the length of the other side. Always fill in the information you have in the following formula:

6.3 Sine and cosine

We learned how to use the tan relationship. Tan uses the opposite side and the adjacent side

 

You can also use the adjacent and the hypotenuse or the opposite side and the hypotenuse to calculate angles. These relationships are called sine (sin) and cosine (cos)

 

You get the sine of an angle by dividing the opposite side by the hypotenuse

sin (x) = opposite:hypotenuse

 

You get the cosine of an angle by dividing the adjacent side by the hypotenuse

cos (x) = adjacent:hypotenuse

 

It's very important to know when you have to use the sine, cosine or tangent... It depends on the information given in the exercise. There are multiple ways to get to know these. Here is a very annoying video where this man put it all in a song for us. I genuinely hope that it helps you and otherwise you have to figure out your own method to remember.

 

SOHCAHTOA

 

Here you can practise using trigometric ratios correctly. The answers are on page 2. Please correct your own work and do not cheat. That is your own responsibility though!

6.4 Calculating in right-angled triangles

Now we also can calculate with sine and cosine in right-angled triangles. In paragraph 6.2 we already practised calculating with the tangent. We just have to know when we use which trigometric ratio we have to use in certain situations. 

 

SOHCAHTOA is very useful in these exercises. The following worksheet is to practise calculating in right-angled triangles.

 

 

 

In a triangle without right angles, you first have to draw an auxiliary line to make a right angle. Often, you can calculate the length of a side or the size of an angle using the sine, cosine or tangent. You can practise this in the next exercises.

 

 

6.5 Angles in solids

The book doesn't give you an elaborate explanation on angles in solids. You have to see triangles within the solids to calculate the line segments and angles you need. The following video gives you a step by step solution to maybe help you see it as well.

 

 

EXTRA: In-depth

History of trigonometry

Click on the link below if you want to do challenge yourself. All the work you will put in now, saves work for the upcoming years. Also you will see that solving some of these problems are just like solving a puzzle. It can be a lot of fun as well!

 

Trigonometry and what else to expect
Khan academy provides courses for mathematicians who are in need of help or want to expand their knowledge of math. All these subjects will also come back in next years when you choose Maths B

EXTRA: Recap

Formative check

Study music