An introduction to the sine, cosine, and tangent functions. Appropriate for students enrolled in algebra, geometry, trig, or precalculus.

1. Melanie Forbes
Basic Trig
Functions
An Introduction to Sine,
Cosine, and Tangent

2. Mosque Detail, provided by Let’s Book (Jamie Carter)
on Flickr, Creative Commons, some rights reserved, April
2009, Seoul, Korea.

3. 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.

4. β 5
3
θ
4
β
7.5
4.5
θ
6
β
10
6
These are 3 similar right triangles;
they each have a 90° angle,
θ equal angles θ, and equal
8 angles β.

5. Comparing Sides β 5
3
 θ
4

6. Comparing Sides β
7.5
4.5

θ
6

7. 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?

8. β
Comparing Sides 6
10
 θ
8

9. The Sine Function

β 5
3
θ
4

10. Mosaic Tile Medallion, provided by A. Davey on flickr,
Creative Commons, Some rights reserved, April 2010,
Mosque, Esfahan, Iran.

11. Practice
 In each triangle, determine sine θ.
 Just click to see the correct answer

12. What is Sine θ?

25
24
θ
7

13. What is Sine θ?

θ 41
9
40

14. What is Sine θ?
5

13
12
θ

15. Left Arrows Reverse Button, Provided by: Microsoft
How did you do?
 Ifyou 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

16. Decorative and Calligraphic Tilewormk, provided by A.
Davey on flickr, Creative Commons, Some rights reserved,
April 2010, Mosque, Esfahan, Iran.

17. The Cosine Function

β 5
3
θ
4

18. Practice
 In each triangle, determine cosine θ.
 Just click to see the correct answer

19. What is Cosine θ?

25
24
θ
7

20. What is Cosine θ?

θ 41
9
40

21. What is Cosine θ?
5

13
12
θ

22. Left Arrows Reverse Button, Provided by: Microsoft
How did you do?
 Ifyou 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

23. 3D Ornamental Mosaic Tile, provided by A. Davey on flickr,
Creative Commons, Some rights reserved, April 2010, Mosque,
Kerman, Iran

24. The Tangent Ratio

β 5
3
θ
4

25. Practice
 In each triangle, determine tangent θ.
 Just click to see the correct answer

26. What is Tangent θ?

25
24
θ
7

27. What is Tangent θ?

θ 41
9
40

28. What is Tangent θ?
5

13
12
θ

29. Left Arrows Reverse Button, Provided by: Microsoft
How did you do?
 Ifyou 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

30. 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

31. Detail 3-D Tilework, provided by A. Davey on flickr, Creative
Commons, Some rights reserved, April 2010, Mosque,
Esfahan, Iran.

32. Detail 3-D Tilework, provided by A. Davey on flickr, Creative
Commons, Some rights reserved, April 2010, Mosque,
Esfahan, Iran.
Thanks for
Watching.
Any idea why I included
pictures from the Middle East?