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Chapter 2

Chapter 2. Acute Angles and Right Triangles. Section 2.1 Trigonometric Functions of Acute Angles. hypotenuse. opposite. A. adjacent. Cofunctions

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Chapter 2

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  1. Chapter 2 Acute Angles and Right Triangles

  2. Section 2.1 Trigonometric Functions of Acute Angles hypotenuse opposite A adjacent

  3. Cofunctions Two trigonometric functions f(x) and g(x) are said to be cofunctions (of each other) if f(A) = g(B) for any pair of complementary angles A and B (i.e. A + B = 90°) Examples: Sine and Cosine, Tangent and Cotangent, Secant and Cosecant. If A + B = 90°, then sin(A) = cos(B), tan(A) = cot(B), sec(A) = csc(B)

  4. Examples Find angle θ in each case. a) cos(θ + 4°) = sin(3θ + 2°) b) tan(2θ – 18°) = cot(θ + 18°)

  5. Trigonometric Function Values of Special Angles

  6. Section 2.2 Trigonometric Functions of Non-Acute Angles Reference Angles Associated with every nonquadrantal angle in standard position is a positive acute angle called its reference angle. A reference angle for an angle θ, written θ’, is the positive acute angle made by the terminal side of the angle θ and the x-axis.

  7. Examples

  8. More Examples

  9. Section 2.3 Finding Trigonometric Function Values Using a Calculator

  10. Section 2.4 Solving Right Triangles Significant digits A number that represents the result of counting is an exact number. There are 50 states in the United States, so in that statement, 50 is an exact number. Most values obtained for trigonometric applications are measured values that are not exact. Suppose that the measurement of our classroom is 15ft by 18ft. The calculation of the diameter is then How many decimal places should we use? Ans: Since the result of the calculation cannot be more accurate than the least accurate measurement, we should indicate that the diameter of the room is approx. 23ft.

  11. Significant Digits The digits obtained by actual measurement are called significant digits. The measurement 18ft is said to have two significant digits; 18.3ft has three significant digits. The following numbers have their significant digits in red. 408 21.518.006.700 0.0025 0.09810 7300

  12. Remember that your answer is no more accurate than the least accurate number in your calculation.

  13. Angle of Elevation and Angle of Depression Example From a window 30.0 ft above the street, the angle of elevation to the top of the building across the street is 50.0°, and the angle of depression of the base of the same building is 20.0°. Find the height of the building.

  14. Section 2.5 Further Applications of Right Triangles Bearing is an important concept in navigation. It uses a single angle to indicate direction, such as 164°, which means that the direction is 164 degrees from due north measured in a clockwise manner.

  15. Example Radar stations A and B are on a east-west line, 3.7 km apart. Station A detects a plane at C, on a bearing of 61°. Station B simultaneously detects the same plane, on a bearing of 331°. Find the distance from A to C.

  16. A second method uses a north-south line and uses an acute angle to show the direction, either east or west, from this line.

  17. Example The bearing from A to C is S 52° E. The bearing from A to B is N 84° E. The bearing from B to C is S 38° W. A plane flying at 250 mph takes 2.4 hr to go from A to B. Find the distance from A to C.

  18. Example 4 Solving a problem involving angles of elevation Francisco needs to know the height of a tree. From a given point on the ground, he finds that the angle of elevation to the top of the tree is 36.7°. He then moves back 50 ft. From the second point, the angle of elevation is 22.2°. Find the height of the tree.

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