7.1 Right Triangle Trigonometry; Applications Objectives
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1 Objectives 1. Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles. Use the Complimentary Angle Theorem 3. Solve Right Triangles 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
2 y = r sin(q) Opposite 7.1 Right Triangle Trigonometry; Applications Right Triangles y (, y) Quadrant I > 0 y > 0 q q = r cos(q) (r, 0) Adjacent Length of side Opposite sin q, cos Length of Hypotenuse tan Length of side Opposite q Length of side Adjacent Length of side Adjacent q Length of Hypotenuse 9 November 017 Kidoguchi, Kenneth
3 Opposite 7.1 Right Triangle Trigonometry; Applications Right Triangles y ( a, b) q q (r, 0) Adjacent a b c 9 November Kidoguchi, Kenneth
4 The Triangle y p/6 p/3 (r, 0) 9 November Kidoguchi, Kenneth
5 The Triangle y p/4 p/4 (r, 0) 9 November Kidoguchi, Kenneth
6 9 November Kidoguchi, Kenneth 7.1 Right Triangle Trigonometry; Applications The Triangle 1 4 cos 1 4 sin p p r r y / r y r r r r y y (r, 0) p/4 p/4 y
7 Right Triangles y y p/6 p/4 3 p/3 1 (, 0) p/4 (, 0) 9 November Kidoguchi, Kenneth
8 1. Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles Find the value of each of the si trigonometric functions of the angle q. 9 November Kidoguchi, Kenneth
9 1. Find the Value of Trigonometric Functions of Acute Angles Using Right Triangles Find the value of each of the si trigonometric functions of the angle q. sin cos 7 q 10 q 1sin q csc 10 q 7 cos q sec q tan q 7 51 cot q November Kidoguchi, Kenneth
10 Constructing a Rain Gutter 9 November Kidoguchi, Kenneth
11 Constructing a Rain Gutter A q A A 4cos q 4sin q 16sin q 16sin q cos q 1 1 Approimate Cross Sectional Area q ( º ) A(q) (in ) b a q A 1 A A 1 9 November Kidoguchi, Kenneth A 1
12 1 1 A1 a b 4cos q 4sin q A 4b 44sinq 7.1 Right Triangle Trigonometry; Applications Constructing a Rain Gutter A q A A 4cos q 4sin q 16sin q 16sin q cos q 1 1 Approimate Cross Sectional Area q ( º ) A(q) (in ) b a q A 1 A A 1 9 November Kidoguchi, Kenneth A 1
13 Constructing a Rain Gutter A q 16sin q cos q 1 Approimate Cross Sectional Area q ( º ) A(q) (in ) November Kidoguchi, Kenneth
14 The Complementary Angle Theorem sin 90º 60º sin 90º cos 60º cos 90º sin 60º sin 30º cos 60º cos 90º 60º cos 90º cos 60º sin 90º sin 60º cos 30º sin 60º 9 November Kidoguchi, Kenneth
15 Naming Convention: Angles, Vertices, Sides Adjacent to A & B Opposite C c B C A a Adjacent to B & C Opposite A b Adjacent to A & C Opposite B 9 November Kidoguchi, Kenneth
16 . Use the Complementary Angle Theorem (a) sin 35 cos 90º? 35º p p p (b) tan cot? 3 3 p p p (c) sec csc? 1 1 (d) cos 5 cos 65? (d) cos 5 cos 65 cos 5 cos90º 65 = cos 5 sin 5 9 November Kidoguchi, Kenneth
17 . Use the Complementary Angle Theorem 9 November Kidoguchi, Kenneth
18 3. Solve Right Triangles º 9 November Kidoguchi, Kenneth
19 3. Solve Right Triangles º B a 8cot 8 tan 35º cos 35º sin 55º 8 c tan tan 7 A cot B B cot A c a 8 c November Kidoguchi, Kenneth
20 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
21 4. Solve Applied Problems 9 November 017 Kidoguchi, Kenneth
22 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
23 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
24 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
25 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
26 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
27 4. Solve Applied Problems 9 November Kidoguchi, Kenneth
14 April Kidoguchi, Kenneth
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