528 CHAPTER 5 Trigonometric Functions The measure of angle A in Figure 7 is 35°. This measure is often expressed by saying that m1angle A2 is 35°, where m1angle A2 is read “the measure of angle A.” The symbolism m1angle A2 = 35° is abbreviated as A = 35°. Traditionally, portions of a degree have been measured with minutes and seconds. One minute, written 1′, is 1 60 of a degree. 1′ = 1 60 ° or 60′ =1° One second, 1″, is 1 60 of a minute. 1″ = 1 60 ′ = 1 3600 ° or 60″ =1′ and 3600″ =1° The measure 12° 42′ 38″ represents 12 degrees, 42 minutes, 38 seconds. A = 35° x y 0 Figure 7 EXAMPLE 4 Converting between Angle Measures (a) Convert 74° 08′ 14″ to decimal degrees to the nearest thousandth. (b) Convert 34.817° to degrees, minutes, and seconds to the nearest second. SOLUTION (a) 74° 08′ 14″ = 74° + 8 60 ° + 14 3600 ° 08′ # 1° 60′ = 8 60 ° and 14″ # 1° 3600″ = 14 3600 ° ≈74° + 0.1333° + 0.0039° Divide to express the fractions as decimals. ≈74.137° Add and round to the nearest thousandth. EXAMPLE 3 Calculating with Degrees, Minutes, and Seconds Perform each calculation. (a) 51° 29′ + 32° 46′ (b) 90° - 73° 12′ SOLUTION (a) 51° 29′ + 32° 46′ 83° 75′ Add degrees and minutes separately. The sum 83° 75′ can be rewritten as follows. 83° 75′ = 83° + 1° 15′ 75′ = 60′ + 15′ = 1° 15′ = 84° 15′ Add. (b) 90° 89° 60′ Write 90° as 89° 60′. - 73° 12′ can be written - 73° 12′ 16° 48′ S Now Try Exercises 41 and 45. An alternative way to measure angles involves decimal degrees. For example, 12.4238° represents 12 4238 10,000 ° .
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