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8.3 trigonometry

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Rana Kkkk
Rana Kkkk

This document introduces trigonometric ratios and their use in right triangles. It discusses how similar right triangles always have equivalent ratios between corresponding sides. Specifically, it shows that the ratio of the opposite side to the hypotenuse of any angle 留 is equal to the sine of that angle. Similarly, the ratio of the adjacent side to the hypotenuse is equal to the cosine of the angle. The document also reviews when to use trigonometric ratios, geometric means ratios, and the Pythagorean theorem to solve for missing terms in right triangles.

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8.3 Trigonometry Done by Rana Karout
Introduction * Opp is abbreviation of Opposite side of angle 40. Are these triangles similar? Why? Find the ratio between the short leg (Opp*) to the hypotenuse in each triangle What do you notice? Opp*/hyp = 0.6427 Use your calculator to find Sine 40
Conclusion (sine) Similar right triangles always have equivalent ratios between corresponding sides. We proved that always (Opp of any angle 留 /Hyp) is equal to specific number which is the sine of this angle So sin 留 = Opp/Hyp
8.3 trigonometry
More trigonometric Ratios Are these triangles similar? Why Find the ratios between the short leg to the hypotenuse in each triangle What do you notice? Can we consider the short leg as an Opp of the angle 55. The short leg is Adjacent (Adj*) to the angle 55 Adj/Hyp = 0.5736 Use your calculator to find Cos 55 * Adj is the abbreviation of Adjacent side of the ngle
Conclusion (Cosine) Similar right triangles always have equivalent ratios between corresponding sides. We prove that always (Adj of any angle 留 /Hyp) is equal to specific number which is the Cos of this angle So Cos 留 = Adj/Hyp
8.3 trigonometry
8.3 trigonometry
SineCosineTangent (Trigonometric Ratios)
Remember Sines and Cosines apply only to right triangles. the opposite side of the right angle is a Hypotenuse. Opposite and Adjacent sides will change according to the acute angle that you refer to. Sines and Cosines values are independent of the dimensions of the triangle. Sine of a 62 degree angle will always be .883, regardless of the size of triangle it is measured in.
Which formula? When? (all in Right triangles) Given Missing term formula Two sides The 3rd side 2 + 2 = 2 Phythagorean Altitude, part of the Hyp The legs or the Hyp Geometric means Ratios One side of special right triangles The other two sides The relation between the sides in special right triangles One side, one angle OR two sides The measures of the triangle (all sides and all angles) Trigonometric Ratios

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8.3 trigonometry

  • 2. Introduction * Opp is abbreviation of Opposite side of angle 40. Are these triangles similar? Why? Find the ratio between the short leg (Opp*) to the hypotenuse in each triangle What do you notice? Opp*/hyp = 0.6427 Use your calculator to find Sine 40
  • 3. Conclusion (sine) Similar right triangles always have equivalent ratios between corresponding sides. We proved that always (Opp of any angle 留 /Hyp) is equal to specific number which is the sine of this angle So sin 留 = Opp/Hyp
  • 5. More trigonometric Ratios Are these triangles similar? Why Find the ratios between the short leg to the hypotenuse in each triangle What do you notice? Can we consider the short leg as an Opp of the angle 55. The short leg is Adjacent (Adj*) to the angle 55 Adj/Hyp = 0.5736 Use your calculator to find Cos 55 * Adj is the abbreviation of Adjacent side of the ngle
  • 6. Conclusion (Cosine) Similar right triangles always have equivalent ratios between corresponding sides. We prove that always (Adj of any angle 留 /Hyp) is equal to specific number which is the Cos of this angle So Cos 留 = Adj/Hyp
  • 10. Remember Sines and Cosines apply only to right triangles. the opposite side of the right angle is a Hypotenuse. Opposite and Adjacent sides will change according to the acute angle that you refer to. Sines and Cosines values are independent of the dimensions of the triangle. Sine of a 62 degree angle will always be .883, regardless of the size of triangle it is measured in.
  • 11. Which formula? When? (all in Right triangles) Given Missing term formula Two sides The 3rd side 2 + 2 = 2 Phythagorean Altitude, part of the Hyp The legs or the Hyp Geometric means Ratios One side of special right triangles The other two sides The relation between the sides in special right triangles One side, one angle OR two sides The measures of the triangle (all sides and all angles) Trigonometric Ratios