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Chapter 5Trigonometric Functions
Section 5.2Trigonometric Functions of Acute Angles
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Trigonometric Functions of Acute Angles
When working with right triangles, it is convenient to refer to the side opposite an angle or the side adjacent to (next to) an angle.
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Trigonometric Functions of Acute Angles
Consider an angle q in the right triangle shown below. Let x and y represent the lengths, respectively, of the adjacent and opposite side of the triangle, and let r be the length of the hypotenuse. Six possible ratios can be formed:
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Trigonometric Functions of Acute Angles
sin q = csc q =
cos q = sec q =
tan q = cot q =
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Trigonometric Functions of Acute Angles
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Example 1
Find the six trigonometric functions of q for the triangle given in the Figure 5.32 below.
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Example 2
Given that q is and acute angle andcos q = , find tan q.
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Trigonometric Functions of Special Angles
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Special Angles
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Trigonometric Functions of Special Angles
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Example
Find the exact value of sin2450 + cos2600.
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Reciprocal Functions
sin q = cos q =
tan q = sec q =
csc q = cot q =
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Applications
From a point 115 feet from the base of a redwood tree, the angle of elevation to the top of the tree is 64.30. Find the height of the tree to the nearest foot.
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Applications
If the distance from a plane to a radar station is 160 miles and the angle of depression is 330, find the number of ground miles from a point directly below the plan to the radar station.
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Applications
The angle of elevation from point A to the top of a space shuttle is 27.20. From a point 17.5 meters further from the space shuttle, the angle of elevation is 23.90. Find the height of the space shuttle.
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Assignment
Section 5.2 - Worksheet