4.3 Right Triangle Trigonometry

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4.3 Right Triangle Trigonometry

• Objectives
• Evaluate trigonometric functions of acute angles
• Use the fundamental trigonometric identities
• Use trigonometric functions to model and solve
  real-life problems

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Trigonometric Functions

• Given a right triangle with acute angle ?

hyp
opp
?
adj
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Example 1

• Evaluate the six trig functions of the angle ?
  shown in the right triangle

• sin ?
• cos ?
• tan ?
• csc ?
• sec ?
• cot ?

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Example 2

• Find the value of x for the right triangle shown

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Example 3

• Solve ?ABC

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You Try

• Solve ?ABC

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Special Triangles30º-60-90
Recall the conversions 30 60
60
2
1
30
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Special Triangles45º-45-90
Recall the conversion 45
45
1
45
1
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Co-functions of Complementary Angles

• Look back at the sines and cosines for the
  30-60-90 triangle
• Note that sin 30cos 60
• Co-functions of complementary angles are
  equivalent

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Trigonometric Identities

• Reciprocal Identities

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Trigonometric Identities

• Quotient Identities

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Trigonometric Identities

• Pythagorean Identities

Note sin2? is (sin ?)2 not sin (?2)
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Example 4

• Given sin?0.6, find the value of cos?
• Given sin?0.6, find the value of tan?

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Example 5

• Use trigonometric identities to transform one
  side of the equation into the other.
• cos?sec?1
• (sec?tan?)(sec?-tan?)1

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Surveying

• A surveyor is standing 50 ft from the base of a
  large tree. The surveyor measures the angle of
  elevation to the top of the tree as 71.5. How
  tall is the tree?

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River Walk

• You are 200 yards from a river. Rather than
  walking directly to the river, you walk 400 yards
  along a straight path to the rivers edge. Find
  the acute angle ? between this path and the
  rivers edge.

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Skateboarding

• Find the length c of the skateboard ramp.

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Homework

• Star Wars Worksheet
• Page 285
• 44-54 even, 79-82 all