�THE BEGINNINGS OF TRIG - TANGENT

OBJECTIVE

• Review over Sine
• Review over Cosine
• Go over Tangent
• Do some examples
• Homework

So to start, let’s begin with �SOHCAHTOA

SOHCAHTOA

A really weird acronym that will help you remember the basic trig functions

Let’s break them down:

S – Sine

O- Opposite

H- Hypotenuse

C- Cosine

A- Adjacent

H – Hypotenuse

T- Tangent

O- Opposite

A- Adjacent

So, what does this all mean?

It means this:

What does that mean?

Basically what we mean is when looking at a triangle, the angle that is being measured has certain sides associated to it.

But, this is easier to show than explain, so here is a triangle:

And here is the angle associated with that triangle

Now, the side that is opposite of this angle is:

The side that is adjacent of this angle is:

And of course, the hypotenuse of this triangle is:

So, in SOHCAHTOA, the sine of an angle is the opposite over the hypotenuse, or:

So, let’s see some examples:

Example 1:

20

35

13

Well, we remember from SOHCAHTOA that:

We can see that the side opposite the angle is 20

And, we can see that the hypotenuse is the biggest side, which we know is 35

So:

Or:

Example 2:

15

22

12

Well, we remember from SOHCAHTOA that:

We can see that the side opposite the angle is 15

And, we can see that the hypotenuse is the biggest side, which we know is 22

So:

Example 3:

16

27

10

Well, we remember from SOHCAHTOA that:

We can see that the side opposite the angle is 16

And, we can see that the hypotenuse is the biggest side, which we know is 27

So:

Now let’s go back to �SOHCAHTOA

SOHCAHTOA

A really weird acronym that will help you remember the basic trig functions

Let’s break them down:

S – Sine

O- Opposite

H- Hypotenuse

C- Cosine

A- Adjacent

H – Hypotenuse

T- Tangent

O- Opposite

A- Adjacent

So, what does this all mean?

It means this:

So, to review, which side is what?

Basically what we mean is when looking at a triangle, the angle that is being measured has certain sides associated to it.

But, this is easier to show than explain, so here is a triangle:

And here is the angle associated with that triangle

Now, the side that is opposite of this angle is:

The side that is adjacent of this angle is:

And of course, the hypotenuse of this triangle is:

So, in SOHCAHTOA, the cosine of an angle is the adjacent over the hypotenuse, or:

So, let’s see some examples:

Example 1:

20

35

13

Well, we remember from SOHCAHTOA that:

We can see that the side that is adjacent of the angle is 20

And, we can see that the hypotenuse is the biggest side, which we know is 35

So:

Or:

Example 2:

15

22

12

Well, we remember from SOHCAHTOA that:

We can see that the side that is adjacent of the angle is 15

And, we can see that the hypotenuse is the biggest side, which we know is 22

So:

Example 3:

16

27

10

Well, we remember from SOHCAHTOA that:

We can see that the side that is adjacent of the angle is 16

And, we can see that the hypotenuse is the biggest side, which we know is 27

So:

Now it gets tricky

Some of you may have noticed that the cosine of some angles are the same as the sine of others.

That’s because sine and cosine are very similar, and the cosine of one angle is the same as the sine of another. �So, when do we use them individually?�Well, that takes time to master, but basically with the right work, you can change them to suit your needs.

Here’s an example:

Example 1:

22

36

16

Well, we remember from SOHCAHTOA that:

We can see that the side that is adjacent of the angle is 22

And, we can see that the hypotenuse is the biggest side, which we know is 36

So:

Or:

Ω

We can see that the side that is opposite of the angle is 22

And, we can see that the hypotenuse is the biggest side, which we know is 36

So:

Or:

IT’S ALL ABOUT PERSPECTIVE

You may find that you can find the answer by taking the sine of some angle.

You may also find that you can find the same answer by taking the cosine of some other angle.

Both are the correct answer.

To prove this, let’s try a few more:

Example 2:

12

19

16

Well, we remember from SOHCAHTOA that:

We can see that the side that is adjacent of the angle is 12

And, we can see that the hypotenuse is the biggest side, which we know is 19

So:

Ω

We can see that the side that is opposite of the angle is 12

And, we can see that the hypotenuse is the biggest side, which we know is 19

So:

Now, for the last time, let’s go back to �SOHCAHTOA

SOHCAHTOA

A really weird acronym that will help you remember the basic trig functions

Let’s break them down:

S – Sine

O- Opposite

H- Hypotenuse

C- Cosine

A- Adjacent

H – Hypotenuse

T- Tangent

O- Opposite

A- Adjacent

So, what does this all mean?

It means this:

One last look at the sides.

Basically what we mean is when looking at a triangle, the angle that is being measured has certain sides associated to it.

But, this is easier to show than explain, so here is a triangle:

And here is the angle associated with that triangle

Now, the side that is opposite of this angle is:

The side that is adjacent of this angle is:

And of course, the hypotenuse of this triangle is:

So, in SOHCAHTOA, the tangent of an angle is the opposite over the adjacent, or:

So, let’s see some examples:

Example 1:

15

20

35

Well, we remember from SOHCAHTOA that:

We can see that the side that is opposite of the angle is 15

And, we can see that the side that is adjacent to the angle is 20

So:

Or:

Example 2:

6

8

10

Well, we remember from SOHCAHTOA that:

We can see that the side that is opposite of the angle is 6

And, we can see that the side that is adjacent to the angle is 8

So:

Or:

Example 3:

9

10

Well, we remember from SOHCAHTOA that:

And, we can see that the side that is adjacent to the angle is 9

So: