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TRIGONOMETRIC RATIOS (DEMO).pptx
- 5. For β π¨, The opposite side is π©πͺ The adjacent side is π¨πͺ For β π©, The opposite side is π¨πͺ The adjacent side is π©πͺ
- 6. Use angle A to name the sides on the following ratios: πππππ ππ‘π βπ¦πππ‘πππ’π π = ππππππππ‘ βπ¦πππ‘πππ’π π = πππππ ππ‘π ππππππππ‘ = βπ¦πππ‘πππ’π π πππππ ππ‘π = βπ¦πππ‘πππ’π π ππππππππ‘ = ππππππππ‘ πππππ ππ‘π = π¨π© π©πͺ π¨πͺ π¨π© π©πͺ π¨πͺ π©πͺ π¨π© π¨π© π¨πͺ π¨πͺ π©πͺ
- 7. Each of the 6 ratios has a name and the names also refer to an angle ππππ ππ β π΄ = πππππ ππ‘π βπ¦πππ‘πππ’π π = πΆππ πππ ππ β π΄ = ππππππππ‘ βπ¦πππ‘πππ’π π = πππππππ‘ ππ β π΄ = πππππ ππ‘π ππππππππ‘ = πΆππ πππππ‘ ππ β π΄ = βπ¦πππ‘πππ’π π πππππ ππ‘π = ππππππ‘ ππ β π΄ = βπ¦πππ‘πππ’π π ππππππππ‘ = πΆππ‘ππππππ‘ ππ β π΄ = ππππππππ‘ πππππ ππ‘π = π¨πͺ π¨π© π©πͺ π¨πͺ π©πͺ π¨π© π¨π© π©πͺ π¨π© π¨πͺ π¨πͺ π©πͺ
- 8. If the angle changes from A to B, the way the ratios are made is the same. ππππ ππ β π΅ = πππππ ππ‘π βπ¦πππ‘πππ’π π = πΆππ πππ ππ β π΅ = ππππππππ‘ βπ¦πππ‘πππ’π π = πππππππ‘ ππ β π΅ = πππππ ππ‘π ππππππππ‘ = πΆππ πππππ‘ ππ β π΅ = βπ¦πππ‘πππ’π π πππππ ππ‘π = ππππππ‘ ππ β π΅ = βπ¦πππ‘πππ’π π ππππππππ‘ = πΆππ‘ππππππ‘ ππ β π΅ = ππππππππ‘ πππππ ππ‘π = π©πͺ π¨π© π¨πͺ π©πͺ π¨πͺ π¨π© π¨π© π¨πͺ π¨π© π©πͺ π©πͺ π¨πͺ
- 9. Each of these ratios has an abbreviation. ππππ ππ β π΄ = πππππ ππ‘π βπ¦πππ‘πππ’π π πΆππ πππ ππ β π΄ = ππππππππ‘ βπ¦πππ‘πππ’π π πππππππ‘ ππ β π΄ = πππππ ππ‘π ππππππππ‘ πΆππ πππππ‘ ππ β π΄ = βπ¦πππ‘πππ’π π πππππ ππ‘π ππππππ‘ ππ β π΄ = βπ¦πππ‘πππ’π π ππππππππ‘ πΆππ‘ππππππ‘ ππ β π΄ = ππππππππ‘ πππππ ππ‘π πΊππβ π¨ πͺππβ π¨ π»ππβ π¨ πͺππβ π¨ πΊππβ π¨ πͺππβ π¨
- 10. ο΅ Sin is Opposite over Hypotenuse S β O β H ο΅ Cos is Adjacent over Hypotenuse C β A β H ο΅ Tan is Opposite over Adjacent T β O β A
- 11. πππβ π΄ = πΆππ β π΄ = πππβ π΄ = πππβ π΅ = πΆππ β π΅ = πππβ π΅ = 6 10 3 5 = 8 10 4 5 = 6 8 3 4 = 8 10 4 5 = 6 10 3 5 = 8 6 4 3 = = o h a h = π a = = o h a h = π a =
- 12. ο΅ Csc is Hypotenuse over Opposite C β H β O ο΅ Sec is Hypotenuse over Adjacent S β H β A ο΅ Cot is Adjacent over Opposite C β A β O
- 13. πΆπ πβ π΄ = πππβ π΄ = πΆππ‘β π΄ = πΆπ πβ π΅ = πππβ π΅ = πΆππ‘β π΅ = 10 6 5 3 = 10 8 5 4 = 8 6 4 3 = 10 8 5 4 = 10 6 5 3 = 6 8 3 4 = = h o β a = π o = = h o β a = π o =
- 14. πππβ π = 3 4 9 12 = o h = πΆππ β π = 1 2 6 12 = a h = πππβ π = 3 2 9 6 = o a = πΆπ πβ π = 4 3 12 9 = h o = πππβ π = 2 12 6 = β a = πΆππ‘β π = 2 3 6 9 = a o =
- 15. ο΅Eratosthenes measured the Sunβs angle at two places in Egypt and used trigonometry to calculate the Earthβs radius.
- 16. ο΅ The heights of the Himalayas were found due to trigonometry. It is not possible for anyone to measure the heights of an entire mountain range, in an age when calculators simply did not exist.
- 19. πππβ π = πΆππ β π = πππβ π = πΆπ πβ π = πππβ π = πΆππ‘β π =
- 20. πππβ π = πΆππ β π = πππβ π = πΆπ πβ π = πππβ π = πΆππ‘β π =
Editor's Notes
- The triangle is one of the most common shapes in nature. You see them almost everywhere that sometimes, you do not notice them anymore. Thre triangle is not only beautiful shape. It has many practical applications in different fields such as in engineering, art, architefcture, astronomy and navigation. Many of these applications make use of the so-called trigonometric ratios. In this topic, you will learn the meanings of these ratios, and use them to solce practical problems.
- Imagine that you, the happy face, are standing at angle A facing into the triangle. The hypotenuse is neither opposite or adjacent. You would be facing the opposite side and standing next to the adjacent side.
- Now, imagine that you move from angle A to angle B still facing into the triangle. Imagine that you, the happy face, are standing at angle A facing into the triangle. The hypotenuse is neither opposite or adjacent. You would be facing the opposite side and standing next to the adjacent side. You would be facing the opposite side and standing next to the adjacent side. Adjacent side Y
- Sine, Cosine and tangent ratios are the most common.
- Hereβs a way to remember how to make the 3 basic trigonometric ratios. The first thing is to identify the Opposite and and Adjacent sides
- SOHCATOA
- Hereβs a way to remember how to make the 3 basic trigonometric ratios. The first thing is to identify the Opposite and and Adjacent sides
- Trigonometry allows you to convert one length to another if you know the angle between them. With trigonometry and a tool called a clinometer you can measure the height of tall objects youβd never be able to measure directly.