trigonometry - A mathematics PowerPoint by Eric Zhao...

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A mathematics PowerPoint by Eric Zhao
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Trigonometry is the study and solution of Triangles. Solving a triangle means finding the value of each of its sides and angles. The following terminology and tactics will be important in the solving of triangles. Pythagorean Theorem (a 2 +b 2 =c 2 ). Only for right angle triangles Sine (sin), Cosecant (csc or sin -1 ) Cosine (cos), Secant (sec or cos -1 ) Tangent (tan), Cotangent (cot or tan -1 ) Right/Oblique triangle
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A trigonometric function is a ratio of certain parts of a triangle. The names of these ratios are: The sine, cosine, tangent, cosecant, secant, cotangent. Let us look at this triangle… a c b ө A B C Given the assigned letters to the sides and angles, we can determine the following trigonometric functions. The Cosecant is the inversion of the sine, the secant is the inversion of the cosine, the cotangent is the inversion of the tangent. With this, we can find the sine of the value of angle A by dividing side a by side c. In order to find the angle itself, we must take the sine of the angle and invert it (in other words, find the cosecant of the sine of the angle). Sinθ= Cos θ= Tan θ= Side Opposite Side Adjacent Side Adjacent Side Opposite Hypothenuse Hypothenuse = = = a b c a b c
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Try finding the angles of the following triangle from the side lengths using the trigonometric ratios from the previous slide. 6 10 8 θ A B C α β Click for the Answer… The first step is to use the trigonometric functions on angle A.
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