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# Trigonometry 1

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Introduction to sine, cosine and tangent

Introduction to sine, cosine and tangent

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### Transcript

• 1.
• 2.
• Explain the term trigonometry.
• Identify the three trigonometric ratios that apply to right angle triangles.
• Calculate values for the three trigonometric ratios that apply to right angled triangles.
• 3.
• Deals with the measurements of the sides and angles of triangles and their relationships with each other.
• For right angled triangles there are six trigonometric ratios that apply.
• We use the following three ratios in the main.
• 4. Sine Ɵ = opposite__ hypotenuse Cosine Ɵ = adjacent__ hypotenuse Tangent Ɵ = opposite adjacent
• 5.
• SOHCAHTOA .
• S ine Ɵ = O pposite___ SOH
• H ypotenuse
• C osine Ɵ = A djacent__ CAH
• H ypotenuse
• T angent Ɵ = O pposite_ TOA
• A djacent
• 6.
• Find the unknown angles in the following triangle.
3m 5m 4m Ø
• 7.
• Since we know the length of each side we can use any of the three ratios to find Ɵ and Ø.
• Sin Ɵ = _ opposite__ = 3m = 0.6
• hypotenuse 5m
• Cos Ɵ = _ adjacent__ = 4m = 0.8
• hypotenuse 5m
• Tan Ɵ = opposite = 3m = 0.75
Ø 5m 4m 3m
• 8.
• To find Ɵ you should use your calculator.
• Sin Ɵ = opposite = 3m = 0.6
• hypotenuse 5m
• Sin Ɵ = 0.6
• Ɵ = Sinˉ¹ 0.6
• Ɵ = 36.87°
5m 4m 3m Ø
• 9.
• Ø can be found from 180 - 90 - 36.87 = 53.13 °
• This can be proved by trigonometry .
• Sin Ø = _ opposite__ = 4m = 0.8 Ø = 53.13 °
• hypotenuse 5m
• Cos Ø = _ adjacent__ = 3m = 0.6 Ø = 53.13 °
• hypotenuse 5m
• Tan Ø = opposite = 4m = 1.33 Ø = 53.13 °