Algebra II B Review 5
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1 Algebra II B Review 5 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the measure of the angle below. y x 40 ο a. 135º b. 50º c. 310º d. 270º Sketch the angle in standard position º a. y c. y 140 ο x 140 ο x
2 b. y d. y 140 ο x 140 ο x 3. Find the cosine and sine of 90º. Round your answers to the nearest hundredth if necessary. y 90 ο x a. 0.71, 0.71 b. 0, 1 c. 0.71, 0.71 d. 1.1, 0 4. Find the exact value of cos 300º and sin 300º. b. d. Write the measure in radians. Express the answer in terms of π º a. b. c. d º a. b. c. d. Write the measure in degrees.
3 7. radians a. 300º b. º c. 5.24º d. º 8. radians a. º b. 144º c. 2.51º d. º Use the graph of y = sin θ to find the value of sin θ for each value of θ º a. 0.4 b. 0.2 c. 0 d radians a. 0.7 b. 0.3 c. 0.9 d Find the period of the graph shown below.
4 a. 2π b. 2 3 π c. 1 2 π d. π 12. Find the amplitude of the sine curve shown below. a. 2π b. 1 c. 0.5 d Sketch one cycle of y = 3 sin 3θ.
5 b. d. 14. Write the equation for the sine function shown below. b. d. 15. Find the period, range, and amplitude of the cosine function. a. b. c. d. Write a cosine function for the graph.
6 16. b. d. 17. Use a graphing calculator to solve the equation in the interval from 0 to 2π. Round to the nearest hundredth. a. 2.41, 4.17 c. 2.30, 3.98 b. 2.20, 4.09 d. 3.80, 2.20, 2.20, Write an equation of the cosine function with amplitude 2 and period 4π. b. d. 19. Use the graph of to find the value of y = tan 1 π. Round to the nearest tenth if necessary. If the 4 tangent is undefined at that point, write undefined. a. 0.4 b. 1 c. 0 d. 2.4
7 20. Sketch the graph of the tangent curve y = tan 1 4 in the interval from 0 to 2π. b. d. 21. Use a graphing calculator to graph the function on the interval and. Evaluate the function at. Round to the nearest tenth. a. 1.7, 1.7, 0 c , 225.2, 0 b , 225.2, 0 d , 225.2, Use the function y = 50 tan x on the interval. Complete the ordered pair (x, 125). Round your answer to the nearest whole number. a. 90º b. 22º c. 2º d. 68º 23. Use a graphing calculator to solve the equation in the interval from. Round your answers to the nearest hundredth. a. 1.21, 4.35 c. 1.21, 2.26, 3.31, 4.35, 5.40 b d , 1,452.5, 3.55, 4.59, Identify the period for and tell where two asymptotes occur for the function. a. period = ; two asymptotes at x = and x =
8 b. c. d. period = ; two asymptotes at x = and x = period = ; two asymptotes at x = and x = 2 period = ; two asymptotes at x = 0 and x = Graph the function in the interval from 0 to 2π. 25. y = 4 cos 4θ b. d. 26. Evaluate cot 105º. Round your answer to the nearest hundredth. a b c d Suppose. Find. a. b. c. d Find the exact value of csc 135º. If the expression is undefined, write undefined. a. 0 b. undefined c. d.
9 29. Find the exact value of sec ( 270º). If the expression is undefined, write undefined. a. undefined b. 1 c. 0 d Find the exact value of cot 45º. If the expression is undefined, write undefined. a. 0 b. 1 c. 1 d. undefined 31. Evaluate to the nearest hundredth. The angle is given in radians. a b c d. 0 Short Answer 32. Consider the graph of the cosine function shown below. a. Find the period and amplitude of the cosine function. b. At what values of for do the maximum value(s), minimum values(s), and zeros occur? 33. a. Sketch at least one cycle of a sine curve with amplitude 4 and period of 1 π. Assume a > 0. 2 b. Write an equation for the graph.
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11 Algebra II B Review 5 Answer Section MULTIPLE CHOICE 1. ANS: C OBJ: Working With Angles in Standard Position STA: MI A MI A ANS: C OBJ: Working With Angles in Standard Position STA: MI A MI A ANS: B OBJ: Using the Unit Circle STA: MI A MI A ANS: B OBJ: Using the Unit Circle STA: MI A MI A ANS: D OBJ: Using Radian Measure STA: MI A MI A ANS: A OBJ: Using Radian Measure STA: MI A MI A ANS: A OBJ: Using Radian Measure STA: MI A MI A ANS: B OBJ: Using Radian Measure STA: MI A MI A ANS: C OBJ: Interpreting Sine Functions 10. ANS: C OBJ: Interpreting Sine Functions 11. ANS: A OBJ: Interpreting Sine Functions 12. ANS: B OBJ: Interpreting Sine Functions 13. ANS: C OBJ: Graphing Sine Functions 14. ANS: A OBJ: Graphing Sine Functions 15. ANS: A OBJ: Graphing and Writing Cosine Functions 16. ANS: D OBJ: Solving Trigonometric Equations 17. ANS: B OBJ: Solving Trigonometric Equations 18. ANS: C OBJ: Solving Trigonometric Equations 19. ANS: B OBJ: Graphing the Tangent Function STA: MI A ANS: C OBJ: Graphing the Tangent Function STA: MI A ANS: B OBJ: Graphing the Tangent Function STA: MI A ANS: D OBJ: Graphing the Tangent Function STA: MI A ANS: B OBJ: Graphing the Tangent Function STA: MI A ANS: C OBJ: Graphing the Tangent Function STA: MI A ANS: C OBJ: Graphing and Writing Cosine Functions
12 26. ANS: B OBJ: Evaluating Reciprocal Trigonometric Functions STA: MI A ANS: C OBJ: Evaluating Reciprocal Trigonometric Functions STA: MI A ANS: D OBJ: Evaluating Reciprocal Trigonometric Functions STA: MI A ANS: A OBJ: Evaluating Reciprocal Trigonometric Functions STA: MI A ANS: B OBJ: Evaluating Reciprocal Trigonometric Functions STA: MI A ANS: A OBJ: Evaluating Reciprocal Trigonometric Functions STA: MI A2.2.6 SHORT ANSWER 32. ANS: a. The period is 1 π and the amplitude is b. maximum values: 0 : 2 π : π : 3 2 π : 2π minimum values: 1 4 π : 3 4 π : 5 4 π : 7 4 π zeros: 1 8 π : 3 8 π : 5 8 π : 7 8 π : 9 8 π : 11 8 π : 13 8 π : 15 8 π OBJ: Graphing and Writing Cosine Functions 33. ANS: a. b. y = 4 sin 4θ OBJ: Graphing Sine Functions
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