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Warm Up(You need a Calculator!!!!!)
Write each fraction as a decimal rounded to the nearest hundredth. Solve each equation. 0.67 0.29 x = 7.25 x = 7.99
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8-2 Trigonometric Ratios Holt Geometry
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A trigonometric ratio is a ratio of two sides of a right triangle.
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SOH CAH TOA
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Example 1A: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. sin J
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Example 1C: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. tan K
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Check It Out! Example 1a Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. cos A
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Example 2: Finding Trigonometric Ratios in Special Right Triangles
Use a special right triangle to write cos 30° as a fraction. Draw and label a 30º-60º-90º ∆.
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Use a special right triangle to write tan 45° as a fraction.
Check It Out! Example 2 Use a special right triangle to write tan 45° as a fraction. s 45° Draw and label a 45º-45º-90º ∆.
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Example 3A: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. sin 52° Be sure your calculator is in degree mode, not radian mode. Caution! sin 52° 0.79
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Example 3C: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. tan 65° tan 65° 2.14
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Check It Out! Example 3a Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. tan 11° tan 11° 0.19
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Find the length. Round to the nearest hundredth.
BC is adjacent to the given angle, B. You are given AC, which is opposite B. Since the adjacent and opposite legs are involved, use a tangent ratio.
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Example 4A Continued Write a trigonometric ratio. Substitute the given values. Multiply both sides by BC and divide by tan 15°. BC ft Simplify the expression.
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Example 4B: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth. QR is opposite to the given angle, P. You are given PR, which is the hypotenuse. Since the opposite side and hypotenuse are involved, use a sine ratio.
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Example 4B Continued Write a trigonometric ratio. Substitute the given values. 12.9(sin 63°) = QR Multiply both sides by 12.9. 11.49 cm QR Simplify the expression.
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11. 12.
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Lesson Quiz: Part I Use a special right triangle to write each trigonometric ratio as a fraction. 1. sin 60° cos 45° Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. 3. tan 84° 4. cos 13° 9.51 0.97
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Lesson Quiz: Part II Find each length. Round to the nearest tenth. 5. CB 6. AC 6.1 16.2 Use your answers from Items 5 and 6 to write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. 7. sin A cos A tan A
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Find each length. Round to the nearest tenth. 1. CB
Warm-Up Find each length. Round to the nearest tenth. 1. CB 2. AC 6.1 16.2 Use your answers from Items 1 and 2 to write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth. 3. sin A cos A tan A 22
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