8.3 trigonometry

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8.3 Trigonometry Done by Rana Karout

Transcript of 8.3 trigonometry

Page 1: 8.3 trigonometry

8.3 Trigonometry

Done by Rana Karout

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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

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Conclusion (sine)

• Similar right triangles always have equivalent ratios between corresponding sides.

• We proved that always (Opp of any angle α /Hyp) is equal to specific number which is the sine of this angle

• So

sin ˂α = Opp/Hyp

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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

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Conclusion (Cosine)

• Similar right triangles always have equivalent ratios between corresponding sides.

• We prove that always (Adj of any angle α /Hyp) is equal to specific number which is the Cos of this angle

• So

Cos ˂α = Adj/Hyp

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Sine–Cosine–Tangent (Trigonometric Ratios)

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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.

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Which formula? When? (all in Right triangles)

• Given • Missing term formula

Two sides The 3rd side 𝑎2 + 𝑏2 = 𝑐2 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