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8 – 6 The Sine and Cosine Ratios

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Sine and Cosine Suppose you want to fine the legs, x and y, in a triangle. You can’t find these values using the tangent ratio because the only side you know it the hypotenuse. The ratios that relate are sine and cosine. Sine = Cosine = hypotenuse Opposite leg Adjacent Leg

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Sine and Cosine We now have 3 useful trigonometric ratios given below Tan A = Sin A = Cos A = SOHCAHTOA

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Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 110.46 or 110 = x 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 120(0.3907) = y 110.46 or 110 = x 120 67 y x

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Sine and Cosine Find the values of x and y to the nearest integer. 120(0.9205) = x 120(0.3907) = y 110.46 or 110 = x y = 46.884 or 47 120 67 y x

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Sine and Cosine Find the value of n to the nearest integer 40 22 n o

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Sine and Cosine Find the value of n to the nearest integer 40 22 n o

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Sine and Cosine Find the value of n to the nearest integer 40 22 n o

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Sine and Cosine Find the value of n to the nearest integer 40 22 n o

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Sine and Cosine Find the value of n to the nearest integer 40 22 n o

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Sine and Cosine Find the value of n to the nearest integer N = 33 40 22 n o

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Triangles. 9.2 The Pythagorean Theorem In a right triangle, the sum of the legs squared equals the hypotenuse squared. a 2 + b 2 = c 2, where a and b.

Triangles. 9.2 The Pythagorean Theorem In a right triangle, the sum of the legs squared equals the hypotenuse squared. a 2 + b 2 = c 2, where a and b.

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