Lessons in Trigonometry

Introduction to Trigonometry

It's Just a Bunch of Fractions!!

In a right triangle you must be able to name the sides. The hypotenuse is easy! But the legs are named by how close they are to the angle we are looking at:

• The side opposite the angle (OPP)

• The side adjacent to the angle (ADJ)

• The hypotenuse (HYP)

Name Sides in Right-Angled Triangles

• The Hypotenuse

• The opposite side

• The adjacent side

Video on how to identify Hypotenuse, Adjacent, and Opposite Sides.

https://youtu.be/ia6sZNjKLw0

Multiple Choice

Which side is adjacent to ∠B?

• AB

• BC

• AC

• ∠C

Multiple Choice

What is the hypotenuse of the triangle shown?

• AB

• BC

• AC

• ∠A

Multiple Choice

What is the side adjacent to ∠A?

• AB

• BC

• AC

• ∠C

Multiple Choice

What is the side opposite ∠A?

• AB

• BC

• AC

• ∠B

Multiple Choice

What is the hypotenuse of the triangle shown?

• AB

• BC

• AC

• ∠A

Setting up your Calculator

IF YOU SKIP THIS STEP ALL YOUR ANSWERS WILL BE WRONG!!!

• Hit the [ON] button

• Hit [MODE]

• Using the arrow keys, move the cursor down and over until it is on top of the word "Degree"

• Hit [Enter]

• "Degree" should now be darkened

• Hit [2ND] then [MODE] ..this is the quit button. Hitting [2nd] activates all the things in yellow above the keys. Quit is in yellow.

Multiple Choice

Lets check to see if you followed all the steps correctly...

Type the following:

SIN 3 0 ) [ENTER]

What should show on your screen is:

sin(30)

Select the number below that you see on your screen.

• 0.5

• -.988031624

Definitions

HOW TO REMEMBER THEM:
SOHCAHTOA

S=O/H C=A/H T=O/A

Putting It Together:

https://youtu.be/n9SgF-iWIaM

Multiple Choice

Determine the value of tan(C)

• 7 / 25

• 24 / 25

• 25 / 7

• 24 / 7

Multiple Choice

Determine the value of sin(C)

• 7 / 25

• 24 / 25

• 25 / 7

• 24 / 7

Multiple Choice

Determine the value of cos(C)

• 7 / 25

• 24 / 25

• 25 / 7

• 24 / 7

Multiple Choice

Find the value of cos(C).

• 29/20

• 21/20

• 20/29

• 20/21

Multiple Choice

Find the value of sin(A). Yes you have to reduce all fractions...

• 3/4

• 5/4

• 5/3

• 4/5

Multiple Choice

Find the value of tan(X). Yes you have to reduce the fractions.

• 3/4

• 4/3

• 5/3

• 3/5

Multiple Choice

Determine the tan(25)

• $$\frac{b}{c}$$

• $$\frac{b}{8}$$
  

• $$\frac{8}{b}$$
  

• $$\frac{c}{8}$$
  

Multiple Choice

What is the cos(25)?

• 
  

  $$\frac{b}{c}$$

• $$\frac{b}{8}$$
  

• $$\frac{c}{8}$$
  

• $$\frac{8}{c}$$
  

Multiple Choice

What is the sin(25)?

• $$\frac{b}{c}$$  

• $$\frac{b}{8}$$
  

• $$\frac{c}{8}$$
  

• $$\frac{8}{c}$$
  

Multiple Choice

Which of the following equations is correct?

• $$\tan\left(15.7\right)=\frac{h}{2.5}$$

• $$\cos\left(15.7\right)=\frac{h}{2.5}$$
  

• $$\sin\left(15.7\right)=\frac{h}{2.5}$$

• None of the above

Using Trig to find Missing Sides

• Label the side of the triangle (hyp, opp, adj)

• Pick a trig ratio (sin, cos, tan) based on what you know and what you want to find

• Write the ratio

• If the variable is on top, multiply; if the variable is on bottom, divide

Poll

If I am given a triangle I can identify the hypotenuse, adjacent, and opposite sides.

• Always

• Most of the time

• Sometime

• Rarely

Poll

If I am given a triangle I can find the sine, cosine, and tangent of an angle.

• Always

• Most of the time

• Sometime

• Rarely

Poll

I can remember the definitions of sine, cosine and tangent

• Yes, it is easy and I can define them without my notes

• If I had my notes I could get it right all the time

• I get confused on which one is which even with my notes

• I have no idea what they are