Geometry (H) Review: Third Quarter Trigonometric Functions 1. Convert each angle in degrees to an equivalent angle in radians. (A) 0 (B) -0 (C) 15 (D) -150 (E) 210 (F) 225 (G) 20 (H) 270 2. Convert each angle in radians to an equivalent measure in degrees. (A) p (B) p 2 (C) - 2 p (D) p (E) 7 p (F) - 5 p (G) p (H) p 2. Evaluate (A) sin p (B) cos 2 p (C) tan 5 p (D) cos - 5 p (E) tan p (F) sin - 5 p (G) cos 7 p (H) tan 2p (I) sin 5 p (J) tan 5 p (K) sin - 2 p (L) cos -p
2 ReviewThirdQuarter.nb Find the amplitude, period, phase shift, and vertical shift of the function, and graph one complete cycle. Label both axes including quarter points on the x-axis.. y = sin 2(x - p ) amp. = period = phase shift = vert. shift = y x. y = 1 + 2 cos 2(x - p ) amp. = period = phase shift = vertical shift = y x
ReviewThirdQuarter.nb Areas and Volumes of Space Figures Find (A) the lateral area, (B) the surface area, and (C) the volume of each figure below. 1. 2. 8 10. 12 9
ReviewThirdQuarter.nb. 10 5. Find (A) the surface area and (B) the volume of the sphere below. ft. The scale factor of two similar solids is :5. If the volume of the smaller figure is find the volume (to the nearest tenth) of the larger figure.
ReviewThirdQuarter.nb 5 Analytic Geometry 1. Find the distance between the points (-1, 1) and (9, -). Express your answer in simplest radical form. 2. Find the coordinates of the midpoint of the segment whose endpoints are A(-2, ) and B(8, -2).. Find the slope of the line that passes through the points C(, -) and D(-10, ). Find an equation of each line described below.. The line that passes through the points (-, ) and (10, -2). 5. The line with slope 5 and y-intercept.. The line with x-intercept - and y-intercept. 7. A line passes through the points (-2, 1) and (, 8). Where does the line intersect the x-axis? the y-axis? 8. Find the magnitude and direction of the vector, -. 9. A vector has magnitude 100 and direction.25 north of west. Express the vector in ordered pair notation.
ReviewThirdQuarter.nb 10. Write an equation of the circle with center (-, ) and radius 5. 11. Write an equation of the circle with center (-2, -) that passes through the point (, 8). 12. Solve the following system of linear equations. 2x + 5y +2z = -5 -x + y +5z = 2 x + y -z = Sets Translate each of the following symbols. 1. 2.. œ. Œ 5. Õ. «7. U 8. n(a) Complete the following theorems. 9. (A B) = 10. (A B) = 11. n(a B) =
ReviewThirdQuarter.nb 7 Classify each of the following as TRUE or FALSE. 12. {1, 2, } Œ {1, 2, } 1. {1, 2, } Õ {1, 2, } 1. English Œ {French, German, Spanish, Englis} 15. { } œ {1, 2,, } 1. «Œ {Curly, Larry, Moe} 17. «Œ «18. «Õ «19. red Õ {red, green, blue} 20. { } = {«} 21. {1} Œ {1, 5, 9} 22. 0 = { } 2. {0} = { } 2. {1} œ {{1}, {2}, {}} 25. n(a B) = n(a) + n(b)
8 ReviewThirdQuarter.nb Use the Venn diagram below to list the sets in roster form. U A 9 B 2 1 5 7 8 12 10 11 C 2. A B 27. A C 28. (B C) 29. A B C 0. (A C) 1. A (B C) Use Venn diagrams to determine whether the following statements are equal for all sets A, B, and C. 2. A (B C), (A B) C. (A B) (B C), B (A C)
ReviewThirdQuarter.nb 9. In a bird sanctuary, 1 different species of birds are being studied. Three large bird feeders are constructed, each providing a different type of bird feed. One feeder has sunflower seeds. A second feeder has a mixture of seeds and te third feeder has small pieces of fruit. The following information was obtained. 20 species ate sunflower seeds. 22 species ate the mixture. 11 species ate the fruit. 10 species ate the sunflower seeds and the mixture. species ate the sunflower seeds and the fruit. species ate the mixture and the fruit. 1 species ate all three. Use a Venn diagram to answer the following questions. How many species ate a) none of the foods? b) the sunflower seeds but neither of the other two foods? c) the mixture and the fruit, but not the sunflower seeds? d) the mixture or the fruit, but not the sunflower seeds? e) exactly one of the foods?