Transcript 4.2 PP
4.2 Trigonometric Functions of Acute Angles Copyright © 2011 Pearson, Inc. What you’ll learn about Right Triangle Trigonometry Two Famous Triangles Evaluating Trigonometric Functions with a Calculator Applications of Right Triangle Trigonometry … and why The many applications of right triangle trigonometry gave the subject its name. Copyright © 2011 Pearson, Inc. Slide 4.2 - 2 Standard Position An acute angle θ is in standard position, when one ray is along the positive x-axis, the vertex is at the origin, and the other ray extends into the first quadrant. Copyright © 2011 Pearson, Inc. Slide 4.2 - 3 Trigonometric Functions Let q be an acute angle in the right DABC. Then opp sine (q ) = sin q = hyp adj cosine (q ) = cosq = hyp opp tangent (q ) = tan q = adj Copyright © 2011 Pearson, Inc. hyp cosecant (q ) = csc q = opp hyp secant (q ) = sec q = adj adj cotangent (q ) = cot q = opp Slide 4.2 - 4 Example Evaluating Trigonometric Functions of 45º Find the values of all six trigonometric functions for an angle of 45º. Copyright © 2011 Pearson, Inc. Slide 4.2 - 5 Example Evaluating Trigonometric Functions of 45º Find the values of all six trigonometric functions for an angle of 45º. Copyright © 2011 Pearson, Inc. Slide 4.2 - 6 Example Evaluating Trigonometric Functions of 60º Find the values of all six trigonometric functions for an angle of 60º. Copyright © 2011 Pearson, Inc. Slide 4.2 - 7 Example Evaluating Trigonometric Functions of 60º Find the values of all six trigonometric functions for an angle of 60º. Copyright © 2011 Pearson, Inc. Slide 4.2 - 8 Common Calculator Errors When Evaluating Trig Functions Using the calculator in the wrong angle mode (degree/radians) Using the inverse trig keys to evaluate cot, sec, and csc Using function shorthand that the calculator does not recognize Not closing parentheses Copyright © 2011 Pearson, Inc. Slide 4.2 - 9 Example Solving a Right Triangle A right triangle with a side length 6 includes a 27º angle adjacent to the side of length 6. Find the measures of the other two angles and the lengths of the other two sides. Copyright © 2011 Pearson, Inc. Slide 4.2 - 10 Example Solving a Right Triangle Copyright © 2011 Pearson, Inc. Slide 4.2 - 11 Quick Review 1. Solve for x. x 2 3 2. Solve for x. 6 x 3 Copyright © 2011 Pearson, Inc. Slide 4.2 - 12 Quick Review 3. Convert 9.3 inches to feet. 4. Solve for a. 5. Solve for b. Copyright © 2011 Pearson, Inc. a 0.45 = 20 36 1.72 = b Slide 4.2 - 13 Quick Review Solutions 1. Solve for x. x 2 x = 13 3 2. Solve for x. 6 x x=3 3 3 Copyright © 2011 Pearson, Inc. Slide 4.2 - 14 Quick Review Solutions 3. Convert 9.3 inches to feet. 4. Solve for a. 5. Solve for b. Copyright © 2011 Pearson, Inc. a 0.45 = 20 36 1.72 = b 0.775 feet 9 900 / 43 » 20.93 Slide 4.2 - 15