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119-0708S-S03-Chapter07 - Applications of Trigonometri c...

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Applications of Trigonometri c Functions Chapter 7
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Right Triangle Trigonometry; Applications Section 7.1
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Trigonometric Functions of Acute Angles Right triangle: Triangle in which one angle is a right angle Hypotenuse: Side opposite the right angle in a right triangle Legs: Remaining two sides in a right triangle
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Trigonometric Functions of Acute Angles Non-right angles in a right triangle must be acute (0 ± < μ < 90 ± ) Pythagorean Theorem: a 2 + b 2 = c 2
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Trigonometric Functions of Acute Angles These functions will all be positive
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Trigonometric Functions of Acute Angles Example. Problem: Find the exact value of the six trigonometric functions of the angle μ Answer:
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Complementary Angle Theorem Complementary angles: Two acute angles whose sum is a right angle In a right triangle, the two acute angles are complementary
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Complementary Angle Theorem
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Complementary Angle Theorem Cofunctions: sine and cosine tangent and cotangent secant and cosecant Theorem . [Complementary Angle Theorem] Cofunctions of complementary angles are equal
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Complementary Angle Theorem Example Problem: Find the exact value of tan 12 ± { cot 78 ± without using a calculator Answer:
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Solving Right Triangles Convention: ® is always the angle opposite side a ¯ is always the angle opposite side b Side c is the hypotenuse Solving a right triangle: Finding the missing lengths of the sides and missing measures of the angles Convention: Express lengths rounded to two decimal places Express angles in degrees rounded to one decimal place
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Solving Right Triangles We know: a 2 + b 2 = c 2 ® + ¯ = 90 ±
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Solving Right Triangles Example. Problem: If b = 6 and ¯ = 65 ± , find a, c and ® Answer:
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Solving Right Triangles Example. Problem: If a = 8 and b = 5, find c, ® and ¯ Answer:
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Applications of Right Triangles Angle of Elevation Angle of Depression
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Applications of Right Triangles Example. Problem: The angle of elevation of the Sun is 35.1 ± at the instant it casts a shadow 789 feet long of the Washington Monument. Use this information to calculate the height of the monument.
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