Lesson 1 Trigonometric Ratios

Last updated 4 months ago

23 Nsɛmmisa

Now that we are good identifying the sides of a right triangle --> Let's now write some Trig ratios with them. Let's do one together on the next slide, before we do some on our own.

Lesson 1 Trigonometric Ratios

Last updated 4 months ago

23 Nsɛmmisa

From the previous slide, manipulate each triangle (red, blue, green) to change their sizes. Take ONE screen shot that includes all three triangles (upload to the show your work area) and fill out the side lengths and ratios (some should be familiar from last class).

RED

(30-60 Right Triangle)

BLUE

(45-45 Right Triangle)

GREEN

(15-75 Right Triangle)

*round to nearest hundredth

In your groups compare your ratio for each triangle (red, blue, green) to your group mates.
a)What do you notice about your ratios compared to your group mates?
b) Why is this the case?

Let's look at the three ratios we found in slide 1 and see if we can use our calculators to find them.

	Ratio from Slide 1	Input in calculator
RED		[sin] 30 =
BLUE		[tan] 45 =
GREEN		[cos] 75=

Ratio from Slide 1

Input in calculator

RED

[sin] 30 =

BLUE

[tan] 45 =

GREEN

[cos] 75=

Welcome to Trigonometry !!!!

Trigonometry is the branch of mathematics dealing with the relationship between side lengths and angle measures of triangles.

Specifically, the Trigonometric Ratios tell us the ratio between two specific sides of a (RIGHT) triangle, given an angle.

We have already seen Trigonometric ratios at play when we looked at the 30 - 60 and 45 -45 right triangles last class.

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the
angle, the relationship between the side opposite the
angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

Your calculator can give you the values of all relations (side ratios), given any angle angle measure. You can use Trig ratios to solve for missing sides or angles of a (right) triangle given some information. For the most part this is just writing and solving proportions for similar triangles (where one ratio is the TRIG ratio and the other ratio is a ratio comparing two sides of the given triangle.)

SOHCAHTOA

For the three main (basic) TRIG ratios will be using: we will use the acronym --> SOHCAHTOA . For these basic trig ratios we will be using RIGHT TRIANGLES ONLY.

SINE =
COSINE =
TANGENT =

Before we attempt to write a TRIG ratio, it is SOOOO important to correctly label the SIDES of the right triangle

Always label the HYPOTENUSE first -->It should be the easiest because it is always opposite the right angle.

Now, the OPPOSITE and ADJACENT side depend where
is located.
("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE
. Then the last side remaining is the ADJACENT side.

Let's practice identifying the sides together on the next slide before we work on our own.

Example. Identifying the sides of a right triangle given

With respect to

is the side.

With respect to

is the

With respect to

is the side.

With respect to

is the side.

With respect to

is the

With respect to

is theside.

With respect to

, which side are the following:

Now that we are good identifying the sides of a right triangle --> Let's now write some Trig ratios with them. Let's do one together on the next slide, before we do some on our own.

Lesson 1 Trigonometric Ratios

Now that we are good identifying the sides of a right triangle --> Let's now write some Trig ratios with them. Let's do one together on the next slide, before we do some on our own.

Lesson 1 Trigonometric Ratios

In your groups compare your ratio for each triangle (red, blue, green) to your group mates.
a)What do you notice about your ratios compared to your group mates?
b) Why is this the case?

Welcome to Trigonometry !!!!

Trigonometry is the branch of mathematics dealing with the relationship between side lengths and angle measures of triangles.

Specifically, the Trigonometric Ratios tell us the ratio between two specific sides of a (RIGHT) triangle, given an angle.

We have already seen Trigonometric ratios at play when we looked at the 30 - 60 and 45 -45 right triangles last class.

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the
angle, the relationship between the side opposite the
angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

SOHCAHTOA

For the three main (basic) TRIG ratios will be using: we will use the acronym --> SOHCAHTOA . For these basic trig ratios we will be using RIGHT TRIANGLES ONLY.

SINE =
COSINE =
TANGENT =

Before we attempt to write a TRIG ratio, it is SOOOO important to correctly label the SIDES of the right triangle

Always label the HYPOTENUSE first -->It should be the easiest because it is always opposite the right angle.

Now, the OPPOSITE and ADJACENT side depend where
is located.
("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE
. Then the last side remaining is the ADJACENT side.

Let's practice identifying the sides together on the next slide before we work on our own.

Example. Identifying the sides of a right triangle given

Now that we are good identifying the sides of a right triangle --> Let's now write some Trig ratios with them. Let's do one together on the next slide, before we do some on our own.

Example: How to write the 3 BASIC TRIG ratios

In your groups compare your ratio for each triangle (red, blue, green) to your group mates.
a)What do you notice about your ratios compared to your group mates?
b) Why is this the case?

Welcome to Trigonometry !!!!

Trigonometry is the branch of mathematics dealing with the relationship between side lengths and angle measures of triangles.

Specifically, the Trigonometric Ratios tell us the ratio between two specific sides of a (RIGHT) triangle, given an angle.

We have already seen Trigonometric ratios at play when we looked at the 30 - 60 and 45 -45 right triangles last class.

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the
angle, the relationship between the side opposite the
angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

SOHCAHTOA

For the three main (basic) TRIG ratios will be using: we will use the acronym --> SOHCAHTOA . For these basic trig ratios we will be using RIGHT TRIANGLES ONLY.

SINE =
COSINE =
TANGENT =

Before we attempt to write a TRIG ratio, it is SOOOO important to correctly label the SIDES of the right triangle

Always label the HYPOTENUSE first -->It should be the easiest because it is always opposite the right angle.

Now, the OPPOSITE and ADJACENT side depend where
is located.
("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE
. Then the last side remaining is the ADJACENT side.

Let's practice identifying the sides together on the next slide before we work on our own.

Example. Identifying the sides of a right triangle given

Example: How to write the 3 BASIC TRIG ratios

Lesson 1 Trigonometric Ratios

Now that we are good identifying the sides of a right triangle --> Let's now write some Trig ratios with them. Let's do one together on the next slide, before we do some on our own.

Lesson 1 Trigonometric Ratios

In your groups compare your ratio for each triangle (red, blue, green) to your group mates. a)What do you notice about your ratios compared to your group mates?b) Why is this the case?

Welcome to Trigonometry !!!!

Trigonometry is the branch of mathematics dealing with the relationship between side lengths and angle measures of triangles.

Specifically, the Trigonometric Ratios tell us the ratio between two specific sides of a (RIGHT) triangle, given an angle.

We have already seen Trigonometric ratios at play when we looked at the 30 - 60 and 45 -45 right triangles last class.

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the angle, the relationship between the side opposite the angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

SOHCAHTOA

For the three main (basic) TRIG ratios will be using: we will use the acronym --> SOHCAHTOA . For these basic trig ratios we will be using RIGHT TRIANGLES ONLY.

SINE = COSINE = TANGENT =

Before we attempt to write a TRIG ratio, it is SOOOO important to correctly label the SIDES of the right triangle

Always label the HYPOTENUSE first -->It should be the easiest because it is always opposite the right angle.

Now, the OPPOSITE and ADJACENT side depend where is located. ("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE . Then the last side remaining is the ADJACENT side.

Let's practice identifying the sides together on the next slide before we work on our own.

Example. Identifying the sides of a right triangle given

Now that we are good identifying the sides of a right triangle --> Let's now write some Trig ratios with them. Let's do one together on the next slide, before we do some on our own.

Example: How to write the 3 BASIC TRIG ratios

In your groups compare your ratio for each triangle (red, blue, green) to your group mates. a)What do you notice about your ratios compared to your group mates?b) Why is this the case?

Welcome to Trigonometry !!!!

Trigonometry is the branch of mathematics dealing with the relationship between side lengths and angle measures of triangles.

Specifically, the Trigonometric Ratios tell us the ratio between two specific sides of a (RIGHT) triangle, given an angle.

We have already seen Trigonometric ratios at play when we looked at the 30 - 60 and 45 -45 right triangles last class.

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the angle, the relationship between the side opposite the angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

SOHCAHTOA

For the three main (basic) TRIG ratios will be using: we will use the acronym --> SOHCAHTOA . For these basic trig ratios we will be using RIGHT TRIANGLES ONLY.

SINE = COSINE = TANGENT =

Before we attempt to write a TRIG ratio, it is SOOOO important to correctly label the SIDES of the right triangle

Always label the HYPOTENUSE first -->It should be the easiest because it is always opposite the right angle.

Now, the OPPOSITE and ADJACENT side depend where is located. ("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE . Then the last side remaining is the ADJACENT side.

Let's practice identifying the sides together on the next slide before we work on our own.

Example. Identifying the sides of a right triangle given

Example: How to write the 3 BASIC TRIG ratios

In your groups compare your ratio for each triangle (red, blue, green) to your group mates.
a)What do you notice about your ratios compared to your group mates?
b) Why is this the case?

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the
angle, the relationship between the side opposite the
angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

SINE =
COSINE =
TANGENT =

Now, the OPPOSITE and ADJACENT side depend where
is located.
("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE
. Then the last side remaining is the ADJACENT side.

In your groups compare your ratio for each triangle (red, blue, green) to your group mates.
a)What do you notice about your ratios compared to your group mates?
b) Why is this the case?

In the 30 -60 Right Triangle, trigonometric ratios tell us that from the
angle, the relationship between the side opposite the
angle (short leg) compared to the hypotenuse is a 1:2 ratio. We will soon define this trigonometric ratio as the SINE ratio.

SINE =
COSINE =
TANGENT =

Now, the OPPOSITE and ADJACENT side depend where
is located.
("theta") is a greek symbol we use in Trigonometry to indicate which angle we are using to establish the ratios.

Personally, I like to locate the OPPOSITE first --> it is located OPPOSITE
. Then the last side remaining is the ADJACENT side.