Trigonometry

Trigonometry

by Uel Roberts - Johnson

Poll

The approach taken with the course has made the work ______________

• Fun

• Easy to understand

• Difficult to understand

• Boring

• I was lost most of the time

Open Ended

I think that the teacher should _______________ to help me better.

​Learning Objectives

​

​By the end of this session, students should be able to:

​

1. ​Recall Pythagoras' Theorem.

2. ​Accurately apply Pythagoras' Theorem to solve 4 questions.

3. ​Recall the Trig Functions.

4. ​Accurately apply the Trig Functions to solve 4 questions.

Before we get started though, tell me three things. Ready? Let's GO!​

Poll

Think about your favorite teacher, what made them your favorite teacher?

• They were bossy.

• They were funny.

• They made class fun and entertaining.

• They were really nice.

Poll

Do what you are supposed to do, when you are supposed to do it, to the best of your ability and you will always find success.

Which part of this statement do you struggle with the most?

• Do what you are supposed to do

• Do it when you are supposed to do it

• Put forth your best effort

• I do not struggle with this statement at all.

Poll

Where would you rather vacation?

I hope you're ready now. . . ​

Let's GO!​

Multiple Choice

What is the name of a triangle with a 90 degree angle?

• 90 triangle

• Left - Angled Triangle

• Right - Angled Triangle

• Normal Triangle

Multiple Choice

The length across from the right angle in a triangle is called the ...........

• cosine

• tangent

• hypotenuse

• sine

Multiple Choice

The name of the longest side of a right angled triangle is the ..........................

• Hypotenuse

• Adjacent

• Hypothesis

Multiple Choice

What is the length of the hypotenuse?

• 16
• 30
• 34

Multiple Select

What are two ways to find missing sides in a right - angled triangle?

• Pythagoras' Theorem

• Trigonometric Functions

• Sine Rule

• Cosine Rule

​Pythagoras Theorem

​

Used to find an unknown side given two sides.

​Let's learn some more!

​Basic Engineering Text page 221

​

​Problems 1 - 3

​

​Page 222, Ex. 89 # 1, 3, 4, 8

​Question 1

​Solving by Pythagoras' Theorem gives:

​

Hypotenuse, h = 41cm

Other side, y = ​40cm

​Unknown side, x = ?

​

​

​Question 3

​Generally....

​The side is named after the angle opposite to it.

Multiple Choice

What is the length of the side opposite ∠X?

• 16
• 30
• 34

​Question 4

​Question 8

​Sides of the triangle are 8, 15 and 17.

​

​The longest side is the hypotenuse, therefore, hypotenuse is 17.

​

​If right - angled then:

​17² = 8² + 15²

​289 = 64 + 225

​289 = 289

​

​Thus, the triangle is a right angle triangle.

​Practice! Practice! Practice!

​Do the following later on to sharpen your skills:

​

​Page 222, Ex. 89 # 2, 6, 10 - 12

​Let's move on . . .

​Trigonometric Functions

• ​When we're given two sides and a missing angle is required, a trig function is used.

• ​Do you recall... (Next 4 slides)

Multiple Choice

What is the saying we use to remember the trig functions?

• SOH CAH TOA

• SAH COH TAO

• COH SAH TOA

• SOH COH TOH

Multiple Choice

$$\sin\theta=$$  

• $$\frac{opposite}{hypotenuse}$$  

• $$\frac{hypotenuse}{opposite}$$  

• $$\frac{adjacent}{hypotenuse}$$  

• $$\frac{opposite}{adjacent}$$  

Multiple Choice

$$\cos\theta=$$  

• $$\frac{opposite}{hypotenuse}$$  

• $$\frac{hypotenuse}{adjacent}$$  

• $$\frac{adjacent}{hypotenuse}$$  

• $$\frac{opposite}{adjacent}$$  

Multiple Choice

$$\tan\theta=$$  

• $$\frac{opposite}{hypotenuse}$$  

• $$\frac{hypotenuse}{adjacent}$$  

• $$\frac{adjacent}{opposite}$$  

• $$\frac{opposite}{adjacent}$$  

​Let's see how it works. . .

​Basic Engineering text page 223, problems 4 - 6... 7Challenge

​

​Practice Ex. 90 # 2 and 4

​Pythagorean Triples

​There are some right angle triangles that are standard. They are sometimes referred to as Pythagorean triples. One of the most common ones is the 3-4-5 triangle. Knowing them can help make your life easier!

​Question 2

​Question 4

​Calculating the magnitude of the angle...

​Page 226, problems 13 and 16

​

​Page 227 Ex. 91 # 6 and 11

​Question 6

​Question 11

Multiple Choice

We can use SOH-CAH-TOA for...

• Any triangle ever
• Non-right triangles only
• Right Triangles only
• Never

Multiple Choice

Solve for the missing angle

• 50
• 0.053
• 36.9
• 95

Missed it? Try again!​

Multiple Choice

Find x.

• 27

• 63

• 24.4

• 65.6

Multiple Choice

Find x.

• 38.7

• 32

• 58

• 51.3

Multiple Choice

Solve for the missing distance.

• 18.9
• 19.5
• 47
• 27.5

Multiple Choice

Solve for the missing angle

• .6 degrees
• .9 degrees
• 36.9 degrees
• 53.1 degrees

Open Ended

One thing you would like to go over . . .