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Math 1316 Section 2.1 Class Notes Trigonometric Functions of Acute Angles Right-Triangle-Based Definition of Trigonometric Functions Note that if θ is an acute angle in standard position and we draw a right triangle as shown in the figure below, then the definition of the six trigonometric functions of θ agree with the previous definition of the six trigonometric ratios given above. Example 1: Find exact values for sin A, cos A, and tan A. B 53 A 45 28 28 C 1 Math 1316 Section 2.1 Class Notes 0 0 Example 2: Find exact value of each expression using the 30 -60 right triangle and isosceles right triangle. 1. cot 300 300 2. cos 600 3. sec 450 450 4. sin 450 2 Math 1316 Section 2.1 Class Notes Example 2: Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using Pythagorean Theorem, and find the exact values of the six trigonometric functions for angle B. 1. a = 3, b = 5 2. b = 8, c = 11 3 Math 1316 Section 2.1 Class Notes Example 3: Write each function in terms of its cofunction. Assume that all unknown appears are acute angles. 1. cot 730 2. cos(α + 200) Example 4: Find one solution for each equation. Assume that all angles in which an unknown appears are acute angles. 1. cos θ = sin 2 θ 2. cot(5θ + 20) = tan(2θ + 40) 4 Math 1316 Section 2.1 Class Notes Trigonometric Function Values of Special Angles Example: Use the table to find: 1. tan 450 2. sin 300 3. csc600 Example: Use calculator to find the approximation to 2 decimal places of the following functions. 1. sin 40o 2. cos 172o 3. sec (-38o) 5 Math 1316 Section 2.1 Class Notes 4. csc(3908o) 5. tan 71o 6. sin 60o Example: Find the exact value of each part labeled with a variable in each figure. 6