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Introduction to sine, cosine and tangent
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1. Explain the term trigonometry.
2. Identify the three trigonometric ratios that apply to right angle triangles.
3. Calculate values for the three trigonometric ratios that apply to right angled triangles.
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.
Sine Ɵ = opposite__ hypotenuse
Cosine Ɵ = adjacent__ hypotenuse
Tangent Ɵ = opposite adjacent
SOHCAHTOA.
Sine Ɵ = Opposite___ SOH Hypotenuse
Cosine Ɵ = Adjacent__ CAH Hypotenuse
Tangent Ɵ = Opposite_ TOA Adjacent
Find the unknown angles in the following triangle.
3m5m
4m
Ø
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 = 0.75adjacent 4m
Ø
5m
4m
3m
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
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°adjacent 3m
3m5m
4m
Ø
Ɵ = 36.87°
Ø = 53.13°
1. Explain the term trigonometry.
2. Identify the three trigonometric ratios that apply to right angle triangles.
3. Calculate values for the three trigonometric ratios that apply to right angled triangles.