Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.
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Transcript of Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.
![Page 1: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/1.jpg)
Basic Trig FunctionsAn Introduction to Sine, Cosine, and Tangent
Melanie Forbes
![Page 2: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/2.jpg)
Mosque Detail, provided by Let’s Book (Jamie Carter) on Flickr, Creative Commons, some rights reserved, April 2009, Seoul, Korea.
![Page 3: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/3.jpg)
What are Trig Functions? Let’s look at 3 similar triangles
If the angles of one triangle are exactly the same as the angles of another, those triangles are similar.
![Page 4: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/4.jpg)
3
4
5
θ
β
6
8
10
θ
β
4.5
6
7.5
θ
β
These are 3 similar right triangles; they each have a 90° angle, equal angles θ, and equal angles β.
![Page 5: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/5.jpg)
Comparing Sides Look at the green triangle and find angle θ Compare the side opposite θ to the
hypotenuse
3
4
5
θ
β
![Page 6: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/6.jpg)
Comparing Sides Look at the taupe triangle and find angle θ Compare the side opposite θ to the
hypotenuse
4.5
6
7.5
θ
β
![Page 7: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/7.jpg)
Ratios are the Same Did you notice that each of the 3 similar
triangles, even though the triangles were different sizes, had the exact same ratio of sides?
![Page 8: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/8.jpg)
Comparing Sides Look at the orange triangle and find angle θ Compare the side opposite θ to the
hypotenuse
6
8
10
θ
β
![Page 9: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/9.jpg)
The Sine Function Ancient mathematicians noticed that
similar right triangles always had side ratios that were the same.
In a right triangle, the ratio of the side opposite a given angle to the hypotenuse is known as the Sine (abbreviated sin) ratio.
Sine θ = In this triangle sin θ = And sin β =
3
4
5
θ
β
![Page 10: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/10.jpg)
Mosaic Tile Medallion, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.
![Page 11: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/11.jpg)
Practice In each triangle, determine sine θ.
Just click to see the correct answer
![Page 12: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/12.jpg)
What is Sine θ?
Sin θ =
7
2425
θ
![Page 13: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/13.jpg)
What is Sine θ?
Sin θ =
9
40
41θ
![Page 14: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/14.jpg)
What is Sine θ?
Sin θ =
5
12
13
θ
![Page 15: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/15.jpg)
How did you do? If you correctly identified the sine ratios
in those triangles, click to move to the next section.
Otherwise, click below to go back.
Go to the beginning Review the sine ratio
Left Arrows Reverse Button, Provided by: Microsoft
![Page 16: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/16.jpg)
Decorative and Calligraphic Tilewormk, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.
![Page 17: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/17.jpg)
The Cosine Function
In a right triangle, the ratio of the side adjacent to a given angle compared to the hypotenuse is known as the Cosine (abbreviated cos) ratio.
Cosine θ = In this triangle cos θ = And cosβ = 3
4
5
θ
β
![Page 18: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/18.jpg)
Practice In each triangle, determine cosine θ.
Just click to see the correct answer
![Page 19: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/19.jpg)
What is Cosine θ?
Cos θ =
7
2425
θ
![Page 20: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/20.jpg)
What is Cosine θ?
Cos θ =
9
40
41θ
![Page 21: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/21.jpg)
What is Cosine θ?
Cos θ =
5
12
13
θ
![Page 22: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/22.jpg)
How did you do? If you correctly identified the cosine
ratios in those triangles, click to move to the next section.
Otherwise, click below to go back.
Review the sine ratio Review the cosine ratio
Left Arrows Reverse Button, Provided by: Microsoft
![Page 23: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/23.jpg)
3D Ornamental Mosaic Tile, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Kerman, Iran
![Page 24: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/24.jpg)
The Tangent Ratio
In a right triangle, the ratio of the side opposite a given angle compared to the side adjacent to the angle is known as the Tangent (abbreviated tan) ratio.
Tangent θ = In this triangle tan θ = And tanβ = 3
4
5
θ
β
![Page 25: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/25.jpg)
Practice In each triangle, determine tangent θ.
Just click to see the correct answer
![Page 26: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/26.jpg)
What is Tangent θ?
Tan θ =
7
2425
θ
![Page 27: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/27.jpg)
What is Tangent θ?
Tan θ =
9
40
41θ
![Page 28: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/28.jpg)
What is Tangent θ?
Tan θ =
5
12
13
θ
![Page 29: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/29.jpg)
How did you do? If you correctly identified the tangent
ratios in those triangles, click to move to the next section.
Otherwise, click below to go back.
Review the cosine ratio
Review the tangent ratio
Left Arrows Reverse Button, Provided by: Microsoft
![Page 30: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/30.jpg)
SOH – CAH - TOA You can remember the definitions of the 3
trig ratios with a mnemonic
SOH: Sin=Opposite/Hypotenuse
CAH: Cos=Adjacent/Hypotenuse
TOA: Tan=Opposite/Adjacent
![Page 31: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/31.jpg)
Detail 3-D Tilework, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.
![Page 32: Basic Trig Functions An Introduction to Sine, Cosine, and Tangent Melanie Forbes.](https://reader037.fdocuments.us/reader037/viewer/2022110213/56649e975503460f94b9aa65/html5/thumbnails/32.jpg)
Thanks for Watching.
Any idea why I included pictures from the Middle East?
Detail 3-D Tilework, provided by A. Davey on flickr, Creative Commons, Some rights reserved, April 2010, Mosque, Esfahan, Iran.