By Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
The eleventh variation of Analytic Trigonometry keeps to provide readers trigonometric innovations and purposes. nearly each proposal is illustrated through an instance through an identical challenge to motivate an energetic involvement within the studying procedure, and inspiration improvement proceeds from the concrete to the summary. large bankruptcy evaluation summaries, bankruptcy and cumulative overview workouts with solutions keyed to the corresponding textual content sections, potent use of colour reviews and annotations, and favorite monitors of vital fabric to assist grasp the topic. Analytic Trigonometry, 11e comprises up-to-date purposes from quite a number various fields.
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Extra info for Analytic Trigonometry with Applications (11th Edition)
Now that we have b, we can use the tangent, cotangent, cosine, or secant to ﬁnd a. 7°) = 101 m cos u = Matched Problem 4 EXAMPLE 5 Solve for a. 7°. Evaluate on a calculator. 4 cm ■ Solving a Right Triangle Solve the right triangle in Figure 6 for u and 90° - u to the nearest 10Ј and for a to three signiﬁcant digits. 7 km Solution Solve for u. 832 sin u = u a FIGURE 6 30 1 RIGHT TRIANGLE RATIOS Given the sine of u, how do we ﬁnd u? We can ﬁnd u directly using a calculator as discussed in Example 3.
There are six possible ratios of the lengths of these three sides. FIGURE 2 Hypotenuse c b Opposite side u b c a c b a c b c a a b a Adjacent side These ratios are referred to as trigonometric ratios, and because of their importance, each is given a name: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). 2) to explain why the value of any of the six trigonometric ratios for that angle is independent of the size of the triangle. cЈ c b u bЈ u a aЈ The trigonometric ratios should be learned.
1° 44. 3 m 23. 5° 24. 8° 25. 8° 26. 3° 27. sec 78°55Ј 28. csc 2°12Ј B In Problems 29–36, ﬁnd each acute angle u to the accuracy indicated. 29. 5 (to the nearest degree) 43. 21 km 45. 8 in. 46. 30 * 106 m 47. 8 ft, c = 134 ft (angles to the nearest 10Ј) 48. 2 km (angles to the nearest 10Ј) 49. b = 132 mi, a = 108 mi 50. 1°) 32 1 RIGHT TRIANGLE RATIOS 51. The graphing calculator screen that follows shows the solution of the accompanying triangle for sides a and b. Clearly, something is wrong. Explain what is wrong and ﬁnd the correct measures for the two sides.