1 of 17

SOH-CAH-TOA

The Gregorian chant of trig

2 of 17

Learning Goals

By the end of the lesson I will be able to:

  • ​
  • ​
  • ​

3 of 17

Labelling Triangles

There are really only 3 things we need to know about labelling triangles:

  • Angles are labelled with ________________________
  • Sides are labelled with _________________________
  • Sides are labelled based on the _____________________

4 of 17

Labelling Triangles

Label both the sides and the angles:

5 of 17

Practice

Fully label the following triangles.

D

E

F

c

b

a

S

R

q

6 of 17

For your Reference

When working with right triangles, we usually pick an angle to use as our reference angle.

It can be whatever angle you want as long as it is ___________________________________.

The reference angle is chosen so that we can talk about sides without being confused.

7 of 17

For your Reference pt. 2

Once we have chosen a reference angle we can then discuss:

  • ​
  • ​
  • ​

… and all of the interesting things that happen when we divide them by each other.

8 of 17

More Visually:

D

E

F

D

E

F

F is our reference angle

E is our reference angle

Remember: Do not use _____ as a reference angle.

9 of 17

Sine

sine (angle) =

Read as: “ ”

The “sine” of an angle tells us the ratio of the side _________________ the angle to the ____________________

On scientific calculators, there is a SIN button, which represents sine.

10 of 17

COSINE

cosine(angle) =

Read as: “ ”

The “cosine” of an angle tells us the ratio of the side _________________ the angle to the ____________________

On scientific calculators, there is a COS button, which represents cosine.

11 of 17

tangent

tangent(angle) =

Read as: “ ”

The “tangent” of an angle tells us the ratio of the side _______________ the angle to side _________________ to the angle.

On scientific calculators, there is a TAN button, which represents tangent.

12 of 17

How can I remember all that?

We have a handy acronym to help us:

- -

Where:

These are called the ________________________________________

13 of 17

Identify the Sides

D

E

F

3

4

5

If F is our reference angle

If E is our reference angle

The opposite side is: __________

The opposite side is: __________

The adjacent side is: __________

The adjacent side is: __________

The hypotenuse is: __________

The hypotenuse is: __________

14 of 17

Fill In the Trig Ratios

D

E

F

3

4

5

sin(F) = 3

sin(E) =

cos(F) = 4

cos(E) =

tan(F) =

4

tan(E) =

15 of 17

Hey, What’s your Sine?

So, sine of an angle represents a ratio. That means it’s just a number.

sin( ) = sin( ) =

sin( ) = sin( ) =

sin( ) = sin( ) =

sin( ) = sin( ) =

​

Sin(any angle) is always less than _______________

16 of 17

Hey, What’s your COSine?

So, sine of an angle represents a ratio. That means it’s just a number. SAME GOES FOR cos!

cos( ) = cos( ) =

cos( ) = cos( ) =

cos( ) = cos( ) =

cos( ) = cos( ) =

​

Cos(any angle) is always less than _______________

17 of 17

Hey, Nice Tan!

So, sine of an angle represents a ratio. That means it’s just a number. SAME GOES FOR cos! And tan!

tan( ) = tan( ) =

tan( ) = tan( ) =

tan( ) = tan( ) =

tan( ) = tan( ) =

​

You can’t take the tangent of angles that are multiples of 90o.