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Published byKristopher Hood Modified over 9 years ago

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Trigonometric Ratios Triangles in Quadrant I

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a Trig Ratio is … … a ratio of the lengths of two sides of a right Δ

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3 Basic Trig Ratios Sine (sin) Cosine (cos) Tangent (tan) These trig ratios (or trig functions) can be used to SOLVE a right triangle … that means to find all the side lengths and angle measures of the right triangle.

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Right Triangles The hypotenuse is opposite the right angle. The shortest side is opposite the smallest angle. The longest side is opposite the largest angle. A b a B

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Sin = Cos = Tan =

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Just remember Chief… SOHCAHTOA ineine ppositepposite ypotenuseypotenuse osineosine djacentdjacent ypotenuseypotenuse angentangent ppositepposite djacentdjacent

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Each trig function has a RECIPROCAL function. sine → cosecant (csc) cosine → secant (sec) tangent → cotangent (cot)

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Six Trig Ratios of Six Trig Ratios of x y r

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Find the ratios for the 6 trig functions. sin = 5/13 cos = 12/13 tan = 5/12 13 12 5 csc = 13/5 sec = 13/12 cot = 12/5

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Find the ratios for the 6 trig functions. sin = 3/5 cos = 4/5 tan = 3/4 csc = 5/3 sec = 5/4 cot = 4/3 Given: csc = 5/3 Use Pythagorean Theorem to find the missing side length!

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Find the ratios for the 6 trig functions. sin α = cos α = tan α = 4 α csc α = sec α = cot α = Given: tan α = 4 Use Pythagorean Theorem to find the missing side length!

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