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Who remembers the Trig Functions? Sine Sine Tangent Tangent Cosine Cosine.

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Presentation on theme: "Who remembers the Trig Functions? Sine Sine Tangent Tangent Cosine Cosine."— Presentation transcript:

1 Who remembers the Trig Functions? Sine Sine Tangent Tangent Cosine Cosine

2 Basic definitions In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b. The shape of a right triangle is completely determined, up to similarity, by the value of either of the other two angles.shaperightsimilarityvalueangles This means that once one of the other angles is known, the ratios of the various sides are always the same regardless of the size of the triangle.ratiostriangle These ratios are traditionally described by the following trigonometric functions of the known angle:ratiostrigonometric functions (2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site:

3 The sine function (sin), defined as the ratio of the leg opposite the angle to the hypotenuse.leg The cosine function (cos), defined as the ratio of the adjacent leg to the hypotenuse. The tangent function (tan), defined as the ratio of the opposite leg to the adjacent leg. The adjacent leg is the side of the angle that is not the hypotenuse. The hypotenuse is the side opposite to the 90 degree angle in a right triangle; it is the longest side of the triangle. ( 2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site:

4 (2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site: In this right triangle: sin(A) = a/c; cos(A) = b/c; tan(A) = a/b. Trig Functions

5 When will we use trig? com/viewVideo.ph p?video_id= &title=Using_Trig _in_Real_Life com/viewVideo.ph p?video_id= &title=Using_Trig _in_Real_Life com/viewVideo.ph p?video_id= &title=Using_Trig _in_Real_Life com/viewVideo.ph p?video_id= &title=Using_Trig _in_Real_Life

6 Do you a have a creative way to remember the ratios?

7 The sine, cosine and tangent ratios in right triangles can be remembered by SOH CAH TOA (sine-opposite-hypotenuse cosine-adjacent-hypotenuse tangent- opposite-adjacent). It is commonly referred to as "Sohcahtoa" by some American mathematics teachers, who liken it to a (nonexistent) Native American girl's or mountain's name.Native American (2007). Trigonometry. Retrieved February 5, 2007, from Wikipedia: The Free Encyclopedia Web site:

8 What about a Δ What about a 45°-45°-90° Δ B A C Sin

9 What about a Δ ? What about a 30°-60°-90° Δ ? A B C Sin

10 Try this one! C B A 6 3 3

11 Look for a pattern:

12 If you find out that the sine of an angle is equal to.5 or ½, what can you say about the angle? What can you say about the triangle if it has a right angle? If the sine of one angle is ½ and the triangle is a right triangle, you have a triangle.

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14 Learn these!!!!


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