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5/5/201510.2: Sine and Cosine Ratios 10.2: Sine and Cosine Expectation: G1.3.1: Define the sine, cosine, and tangent of acute angles in a right triangle as ratios of sides. Solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles. G1.3.3: Determine the exact values of sine, cosine, and tangent for 0°, 30°, 45°, 60°, and their integer multiples and apply in various contexts. L1.1.6: Explain the importance of the irrational numbers √2 and √3 in basic right triangle trigonometry

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Quiz 6/3 Determine the area of the triangle below.

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5/5/201510.2: Sine and Cosine Ratios Sine Ratio Defn: In a right triangle with acute angle, ∠ A, whose measure is θ, the sine of ∠ A (sin ∠ A = sin A = sin θ), is the ratio of the length of the leg opposite ∠ A to the length of the hypotenuse.

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5/5/201510.2: Sine and Cosine Ratios Sine A B C sin A = opposite hypotenuse = a c a b c

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5/5/201510.2: Sine and Cosine Ratios Sine A B C sin B = opposite hypotenuse = b c a b c

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5/5/201510.2: Sine and Cosine Ratios Cosine Ratio Defn: In a right triangle with acute angle, ∠ A, whose measure is θ, the cosine of ∠ A (cos ∠ A = cos A = cos θ), the ratio of the length of the leg adjacent to ∠ A to the length of the hypotenuse.

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5/5/201510.2: Sine and Cosine Ratios Cosine cos A = adjacent hypotenuse = b c A B C a b c

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5/5/201510.2: Sine and Cosine Ratios Cosine cos B = adjacent hypotenuse = a c A B C a b c

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5/5/201510.2: Sine and Cosine Ratios What are the sin and cos of ∠ B? A C B 20 12 16

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5/5/201510.2: Sine and Cosine Ratios For the right triangle shown below, what is the sin C? a. a / b b. a / c c. b / a d. c / b e. c / a A C B a b c

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5/5/201510.2: Sine and Cosine Ratios 45 Give the exact sin, cos and tan of a 45 degree angle.

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5/5/201510.2: Sine and Cosine Ratios Give the exact sin, cos and tan of a 30 and 60 degree angle. 30 60

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5/5/201510.2: Sine and Cosine Ratios If AC = 10 in the figure below, determine BD. 5/5/2015Trig Basics 45° 30°

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5/5/201510.2: Sine and Cosine Ratios sohcahtoa opposite hypotenuse sin = adjacent hypotenuse cos = opposite adjacent tan =

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5/5/201510.2: Sine and Cosine Ratios If cos A = 4 / 5 and sin A = 3 / 5, then tan A = ? A.¾ B. 3 / 5 C. 4 / 5 D. 4 / 3 E. 12 / 5

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5/5/201510.2: Sine and Cosine Ratios On a Calculator sin returns the sine ratio of a given angle sin -1 returns the angle measure with a given sine ratio.

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5/5/201510.2: Sine and Cosine Ratios On a Calculator cos returns the cosine ratio of a given angle cos -1 returns the angle measure with a given cosine ratio.

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Give the exact sine, cosine and tangent for a 60 degree angle. Make sure you label each answer and do not talk.

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5/5/201510.2: Sine and Cosine Ratios Determine the value of x below. Round your answer to the nearest tenth. 20 x 34°

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5/5/201510.2: Sine and Cosine Ratios What is the value of x below (to the nearest tenth)? 43 54° x

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5/5/201510.2: Sine and Cosine Ratios Calculate θ below to the nearest tenth. θ 20 43

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5/5/201510.2: Sine and Cosine Ratios Angles of Elevation θ Looking up from the horizontal

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5/5/201510.2: Sine and Cosine Ratios Angles of Depression θ Looking down from the horizontal

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5/5/201510.2: Sine and Cosine Ratios A kite is at the end of a 100’ string. If the string makes an angle of elevation of 73°, how high to the nearest inch is the kite?

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5/5/201510.2: Sine and Cosine Ratios Identities An identity is an equation that is true for all values of the variables. ex: (a+b) 2 = a 2 + 2ab + b 2 ex: a 2 – b 2 = (a + b)(a – b)

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5/5/201510.2: Sine and Cosine Ratios Trig Identities a. tan θ = sin θ cos θ b. sin 2 θ+ cos 2 θ = 1

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5/5/201510.2: Sine and Cosine Ratios pages 644 – 645, #11 – 35, (odds), 36 - 43 (all), 45, 47, 49 - 51 (all) Assignment

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Warm – up Find the sine, cosine and tangent of angle c.

Warm – up Find the sine, cosine and tangent of angle c.

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