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Published byBraulio Beachley Modified about 1 year ago

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13.6 – The Tangent Function

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The Tangent Function Use a calculator to find the sine and cosine of each value of . Then calculate the ratio. 1. radians2.30 degrees 3.90 degrees4. radians 5. radians6.0 degrees sin cos

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The Tangent Function 1.Sin 0.866; cos = 0.5; sin 30° = 0.5; cos 30° 0.866; sin 90° = 1; cos 90° = 0; =, undefined 33 sin 3 cos sin 30° cos 30° sin 90° cos 90° 1010 Solutions

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The Tangent Function 4.sin = 0.5; cos –0.866; – sin = 1; cos = 0; =, undefined 6.sin 0° = 0; cos 0° = 1; = = sin 5 6 cos – sin 5 2 cos sin 0° cos 0° 0101 Solutions (continued)

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The Tangent Function Use the graph of y = tan to find each value. a. tan –45°tan –45° = –1 b. tan 0° tan 0° = 0 c. tan 45°tan 45° = 1

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Sketch the asymptotes. The Tangent Function Sketch two cycles of the graph y = tan. period = Use the formula for the period. b = = 2 Substitute for b and simplify One cycle occurs in the interval – to. Plot three points in each cycle. Sketch the curve. Asymptotes occur every 2 units, at = –,, and 3. 2

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The Tangent Function What is the height of the triangle, in the design from Example 3, when = 18°? What is the height when = 20°? Step 1: Sketch the graph.Step 2: Use the TABLE feature. When = 18°, the height of the triangle is about 32.5 ft. When = 20°, the height of the triangle is about 36.4 ft.

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