By Colin Adams, Jon Rogawski
The main profitable calculus ebook of its new release, Jon Rogawski’s Calculus bargains a terrific stability of formal precision and devoted conceptual concentration, supporting scholars construct robust computational abilities whereas always reinforcing the relevance of calculus to their destiny experiences and their lives.
Guided by means of new writer Colin Adams, the hot variation remains precise to the overdue Jon Rogawski’s fresh and powerful technique, whereas drawing on broad teacher and pupil suggestions, and Adams’ 3 a long time as a calculus instructor and writer of math books for common audiences.
W. H. Freeman/Macmillan and WebAssign have partnered to convey WebAssign top class – a entire and versatile suite of assets to your calculus direction. Combining the main prevalent on-line homework platform with the authoritative and interactive content material from the textbook, WebAssign top rate extends and complements the study room event for teachers and scholars.
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Extra resources for Calculus: Early Transcendentals (3rd Edition)
Example text
29. Find the values of sin θ , cos θ , and tan θ for the angles corresponding to the eight points on the unit circles in Figure 23(A) and (B). 918) 8. Find the values of the six standard trigonometric functions at θ = 11π/6. In Exercises 9–14, use Figure 22 to find all angles between 0 and 2π satisfying the given condition. 9. cos θ = 1 2 (A) (B) FIGURE 23 10. tan θ = 1 11. tan θ = −1 √ 3 13. sin x = 2 30. Refer to Figure 24(A). Express the functions sin θ , tan θ , and csc θ in terms of c. 12.
E X A M P L E 4 Trigonometric Equation sin θ1 Solution We must find the angles x such that sin 4x = − sin 2x. First, let’s determine when angles θ1 and θ2 satisfy sin θ2 = − sin θ1 . Figure 13 shows that this occurs if θ2 = −θ1 or θ2 = θ1 + π . Because the sine function is periodic with period 2π , θ1 θ1 sin θ2 = − sin θ1 ⇔ θ2 = −θ1 + 2π k or θ2 = θ1 + π + 2π k where k is an integer. Taking θ2 = 4x and θ1 = 2x, we see that θ2 = θ1 + π θ2 = −θ1 sin 4x = − sin 2x −sin θ1 θ2 = −θ1 or θ2 = θ1 + π .
4 17. f (x) = x2 x + sin x 34. f (t) = 18. f (x) = 2x 2x 3 + 3x 19. f (x) = 9 − 7x 2 3x − 9x −1/2 20. f (x) = 9 − 7x 2 21. f (x) = sin(x 2 ) x 22. f (x) = √ x+1 23. f (x) = x 2 + 3x −1 24. f (x) = sin(3x ) √ t, In Exercises 27–34, calculate the composite functions f ◦ g and g ◦ f , and determine their domains. √ 27. f (x) = x, g(x) = x + 1 g(x) = x −4 g(x) = x 2 30. f (x) = |x|, g(θ ) = sin θ 1 32. f (x) = 2 , x +1 1 33. f (t) = √ , t 3 when x < 0 x 2 + 3 when x ≥ 0 f (x) = x + 1 when x < 0 1 − x when x ≥ 0 f (x) = x2 −x 2 37.