586 CHAPTER 5 Trigonometric Functions Concepts Examples To find the corresponding angle measure given a trigonometric function value, use an appropriate inverse function. Find an angle u in the interval 30° , 90°2 that satisfies each condition in color. cos u ≈0.73677482 u ≈cos-110.736774822 u ≈42.542600° csc u ≈1.04766792 sin u ≈ 1 1.04766792 u ≈sin-1 a 1 1.04766792b u ≈72.65° Solutions and Applications of Right Triangles Solving an Applied Trigonometry Problem Step 1 Draw a sketch, and label it with the given information. Label the quantity to be found with a variable. Step 2 Use the sketch to write an equation relating the given quantities to the variable. Step 3 Solve the equation, and check that the answer makes sense. Expressing Bearing Use one of the following methods. Method 1 When a single angle is given, bearing is measured in a clockwise direction from due north. Method 2 Start with a north-south line and use an acute angle to show the direction, either east or west, from this line. Find the angle of elevation of the sun if a 48.6-ft flagpole casts a shadow 63.1 ft long. Step 1 See the sketch. We must find u. u Shadow 63.1 ft Flagpole 48.6 ft Sun Step 2 tan u = 48.6 63.1 tan u ≈0.770206 Step 3 u = tan-1 0.770206 u ≈37.6° The angle of elevation rounded to three significant digits is 37.6°, or 37° 40′. Consider the following. Example: 220° Example: S 40° W 2208 N 408 S 5.4 sin u = 1 csc u
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