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# Lesson 68 Trigonometric Ratios

Trigonometry lesson with SohCahToa for Geometry

by

Tweet## Brandon Johnson

on 11 March 2013#### Transcript of Lesson 68 Trigonometric Ratios

Trigonometry Trigonometry deals with a special kind of triangle called a RIGHT TRIANGLE Trig Functions Sine Cosine Tangent Each trig function is a ratio comparing a specific side length to another side length leg leg hypotenuse sides touching

right angle longest side a b c if i am angle θ θ a opposite b adjacent c hypotenuse SOH Sin = Opposite Hypotenuse θ o

p

p hyp hyp θ Adjacent Cos = CAH adj Hypotenuse Adjacent TOA Opposite o

p

p Tan = θ adj SOHCAHTOA what is the sine of angle θ? what is the cosine of angle θ? what is the tangent of angle θ? a c b θ c a θ b c a θ b c a θ b b c a θ a c b θ Examples Find Sin(θ) θ 8 6 10 θ θ 4 4.5 2 7.2 10 7 Find cos(θ) 1) 6/10 = 0/6 = 3/5

2) 2/4.5 = 0.44 = 4/9

3) 7/7.2 = 0.97 = 35/36 1) 2) 3) θ 16 65 63 45 36 θ 27 θ 1) 35/37 = 0.95 = 35/37

2) 36/45 = 0.8 = 4/5

3) 63/65 = 0.97 = 63/65 Find tan(θ) 35 37 12 θ θ θ 13 12 5 24 26 10 21 20 29 side

length side

length side

length a/c b/c b/c a/c a/b b/a 1) 24/10 = 2.4 = 12/5

2) 5/12 = 0.42 = 5/12

3) 21/20 = 1.05 = 21/20 3) 2) 1) 1) 2) 3) If you're given an angle measurement, use a calculator to determine the value. Step 1: Press 2nd key

Step 2: Press TRIG key

Use the arrows to select the desired trig function with the cursor.

Step 3: Enter degree value PRESS ENTER! PRESS ENTER! Step 1: Press TRIG key

Step 2: Enter degree value Find sin 45° sin 45°= 0.707 Find cos 30° cos 30°= 0.866 Find tan 47° tan 47°= 1.072 Solve for side length x 5 x 30° if i'm angle 30°

what side relations

do i have? x is opposite

5 is hypotenuse use Sine! which trig function? sin 30°= x/5 multiply both sides by 5! 5 * sin 30°= x 5 * 0.5 = x x = 2.5 which trig function? 9 is opposite

15 is adjacent if i'm angle x°

what side relations

do i have? 15 x° Solve for angle x° 9 tangent! tan x°= 9/15 when looking for an angle,

you must use the

Inverse Trig Functions take tan of both sides x°= tan (9/15) x°= 30.96° -1 -1 sin cos tan -1 -1 -1 put in calculator a boy is standing 65 ft.

from a side of a building and is staring at the top at an angle of 40°

how tall is the building? 65 ft. x ft. 40° is is is the building is 54.5 ft. tall Test Day and Trig Day

Warmup

1. Get ready for your test!

2. 3-5 minutes to prepare for your test

3. If you have questions, ask coacha Day 2 http://www.wisc-online.com/objects/ViewObject.aspx?ID=TMH601 More practice Homework

(2 worksheets) EQ: How can the ratios

discussed previously help

us in finding specific

information?

(Warm-up on the board) Character

Development Humble

Beginnings

BLUEFISHTV Day 3

1. Solve for the following

problems put on the board. EQ:

How can story problems be so easy a cave man can do it? Step #1

Draw a picture! Step #2

Figure out what you have and what you are missing. Step #3

Solve for the missing side. •1. Take out HW and Quiz and start working on them•

2. If you were at the game, come up and prove that to coach j. at the beginning of class That is all Folks!!!!

(Real World Problems) Beth Reynolds-- You make the criteria for how we will grade the following project 1. I am going to hand out a sheet for the following trigonometry project.

2. We will then come up with ways that we will assess the project. 3.After we figure out criteria, we will then start on the project in groups of two.

4. This project will be due on the day of the review for our first test grade. Warm-up Review Game:

Bonus for the team who wins!!! (for quiz)

Warm-up:

• Take out both assignments (Get ready to switch it with someone next to you) Make sure to check

2 HW assignments.

Make sure to collect

projects. Today and Friday

Lesson 66 Part 2 Part 1 Part 3 Part 4 Make sure to view podcast on the day I am missing! Schedule this Week:

Monday: Review over Trig.

Tuesday: Lesson 73

Wed./Thurs.: Trig. Project

Friday: Test over Trig. character development

podcast Homework

Quiz

Trigonometry Find the sine of a 60 degree angle. For the remaining time, work on your trigonometry worksheet and quiz.

(Q's Ask Coach J.) What are the trigonometric ratios? Label the angle of depression and angle of elevation. GO BLUE!!!!! REVIEW Lesson 73 (Trig. Part 2) Homework:

Trigonometry

Worksheet

Illustration Instructions:

*The first one to figure out the following problems win HW passes. Vo Yo Mama Vocabulary Section The angle below horizontal that an observer must look to see an object that is lower than the observer. Angle of Depression Angle of Elevation The angle above horizontal that an observer must look to see an object that is higher than the observer. 1. 2. http://www.facebook.com/pages/Greater-Atlanta-Christian-School/390625947525?fref=ts CLINOMETER Announcements

--> Activity

--> Stuff to Bring

--> HW

Full transcriptright angle longest side a b c if i am angle θ θ a opposite b adjacent c hypotenuse SOH Sin = Opposite Hypotenuse θ o

p

p hyp hyp θ Adjacent Cos = CAH adj Hypotenuse Adjacent TOA Opposite o

p

p Tan = θ adj SOHCAHTOA what is the sine of angle θ? what is the cosine of angle θ? what is the tangent of angle θ? a c b θ c a θ b c a θ b c a θ b b c a θ a c b θ Examples Find Sin(θ) θ 8 6 10 θ θ 4 4.5 2 7.2 10 7 Find cos(θ) 1) 6/10 = 0/6 = 3/5

2) 2/4.5 = 0.44 = 4/9

3) 7/7.2 = 0.97 = 35/36 1) 2) 3) θ 16 65 63 45 36 θ 27 θ 1) 35/37 = 0.95 = 35/37

2) 36/45 = 0.8 = 4/5

3) 63/65 = 0.97 = 63/65 Find tan(θ) 35 37 12 θ θ θ 13 12 5 24 26 10 21 20 29 side

length side

length side

length a/c b/c b/c a/c a/b b/a 1) 24/10 = 2.4 = 12/5

2) 5/12 = 0.42 = 5/12

3) 21/20 = 1.05 = 21/20 3) 2) 1) 1) 2) 3) If you're given an angle measurement, use a calculator to determine the value. Step 1: Press 2nd key

Step 2: Press TRIG key

Use the arrows to select the desired trig function with the cursor.

Step 3: Enter degree value PRESS ENTER! PRESS ENTER! Step 1: Press TRIG key

Step 2: Enter degree value Find sin 45° sin 45°= 0.707 Find cos 30° cos 30°= 0.866 Find tan 47° tan 47°= 1.072 Solve for side length x 5 x 30° if i'm angle 30°

what side relations

do i have? x is opposite

5 is hypotenuse use Sine! which trig function? sin 30°= x/5 multiply both sides by 5! 5 * sin 30°= x 5 * 0.5 = x x = 2.5 which trig function? 9 is opposite

15 is adjacent if i'm angle x°

what side relations

do i have? 15 x° Solve for angle x° 9 tangent! tan x°= 9/15 when looking for an angle,

you must use the

Inverse Trig Functions take tan of both sides x°= tan (9/15) x°= 30.96° -1 -1 sin cos tan -1 -1 -1 put in calculator a boy is standing 65 ft.

from a side of a building and is staring at the top at an angle of 40°

how tall is the building? 65 ft. x ft. 40° is is is the building is 54.5 ft. tall Test Day and Trig Day

Warmup

1. Get ready for your test!

2. 3-5 minutes to prepare for your test

3. If you have questions, ask coacha Day 2 http://www.wisc-online.com/objects/ViewObject.aspx?ID=TMH601 More practice Homework

(2 worksheets) EQ: How can the ratios

discussed previously help

us in finding specific

information?

(Warm-up on the board) Character

Development Humble

Beginnings

BLUEFISHTV Day 3

1. Solve for the following

problems put on the board. EQ:

How can story problems be so easy a cave man can do it? Step #1

Draw a picture! Step #2

Figure out what you have and what you are missing. Step #3

Solve for the missing side. •1. Take out HW and Quiz and start working on them•

2. If you were at the game, come up and prove that to coach j. at the beginning of class That is all Folks!!!!

(Real World Problems) Beth Reynolds-- You make the criteria for how we will grade the following project 1. I am going to hand out a sheet for the following trigonometry project.

2. We will then come up with ways that we will assess the project. 3.After we figure out criteria, we will then start on the project in groups of two.

4. This project will be due on the day of the review for our first test grade. Warm-up Review Game:

Bonus for the team who wins!!! (for quiz)

Warm-up:

• Take out both assignments (Get ready to switch it with someone next to you) Make sure to check

2 HW assignments.

Make sure to collect

projects. Today and Friday

Lesson 66 Part 2 Part 1 Part 3 Part 4 Make sure to view podcast on the day I am missing! Schedule this Week:

Monday: Review over Trig.

Tuesday: Lesson 73

Wed./Thurs.: Trig. Project

Friday: Test over Trig. character development

podcast Homework

Quiz

Trigonometry Find the sine of a 60 degree angle. For the remaining time, work on your trigonometry worksheet and quiz.

(Q's Ask Coach J.) What are the trigonometric ratios? Label the angle of depression and angle of elevation. GO BLUE!!!!! REVIEW Lesson 73 (Trig. Part 2) Homework:

Trigonometry

Worksheet

Illustration Instructions:

*The first one to figure out the following problems win HW passes. Vo Yo Mama Vocabulary Section The angle below horizontal that an observer must look to see an object that is lower than the observer. Angle of Depression Angle of Elevation The angle above horizontal that an observer must look to see an object that is higher than the observer. 1. 2. http://www.facebook.com/pages/Greater-Atlanta-Christian-School/390625947525?fref=ts CLINOMETER Announcements

--> Activity

--> Stuff to Bring

--> HW