Algebra 2B: Trigonometry Unit Test practice Part 1 Without Calculator, Part 2 with Calculator

Transcription

1 Name: Class: Date: Algebra 2B: Trigonometry Unit Test practice Part 1 Without Calculator, Part 2 with Calculator Short Answer 1. Determine whether the function shown below is or is not periodic. If it is, find the period. 2. Find the exact value of cos 330º and sin 330º. Write the measure in radians. Express the answer in terms of π º Write the measure in degrees. 4. 5π 3 radians Use the graph to find the value of y = sin θ for the value of θ º 1

2 Name: 6. Find the period of the graph shown below. 7. A particular sound wave can be graphed using the function y = 10 sin 2x. Find the amplitude and period of the function. 8. Sketch one cycle of y = 2 sin 3θ. 9. Write the equation for the sine function shown below. 2

3 Name: Write a cosine function for the graph Sketch the graph of the tangent curve y = tan 1 x in the interval from 0 to 2π Identify the period for y = tan 3π 4 θ and tell where two asymptotes occur for the function. 13. Part 2: You may use your calculator for this part of the test. Evaluate csc π 2 to the nearest hundredth. The angle is given in radians. 14. For an angle in standard position measuring 92º, find the values of cosθ and sinθ. Round your answers to the nearest hundredth. 15. Suppose you are building a rain shelter for a local park. The function y = 5 csc θ models the length of rafters y needed if the peak is 5 feet above the top of the wall. The angle θ is formed by the rafters and top of the wall. Use a graphing calculator. Find the length of the rafters needed to make the roof with for θ = 18º. Round to the nearest tenth of a foot. 3

4 Name: 16. Use a graphing calculator to find the solution to the equation 2 cos x = sin x in the interval 0 x 180. (Hint: graph y = 2cos x and y = sin x on the same grid.) 17. The line of sight from a small boat to the light at the top of a 50-foot lighthouse built on a cliff 20 feet above the water makes a 41 angle with the water. To the nearest foot, how far is the boat from the cliff? 18. In XYZ, Y is a right angle and sin X = 14. Find cos X in fraction and in decimal form. Round to the 50 nearest hundredth, if necessary. 19. Find the length x. Round to the nearest tenth. 4

5 Name: Find the measure of x in the right triangle. 22. Use the circle below. Find the length s to the nearest tenth. 23. Find the area of the triangle. Round your answer to the nearest tenth. 5

6 Name: 24. Use the Law of Sines. Find b to the nearest tenth. 25. Use the Law of Cosines. Find b to the nearest tenth. 6

7 Algebra 2B: Trigonometry Unit Test practice Part 1 Without Calculator, Part 2 with Calculator Answer Section SHORT ANSWER 1. ANS: periodic; about 6 PTS: 1 DIF: L2 REF: 13-1 Exploring Periodic Data OBJ: Identifying Periodic Functions TOP: 13-1 Example 2 KEY: cycle period periodic function 2. ANS: cos = 1 2, sin = 3 2 PTS: 1 DIF: L2 REF: 13-2 Angles and the Unit Circle OBJ: Using the Unit Circle TOP: 13-2 Example 5 KEY: unit circle cosine of an angle sine of an angle 3. ANS: π 6 x5 PTS: 1 DIF: L2 REF: 13-3 Radian Measure OBJ: Using Radian Measure TOP: 13-3 Example 1 KEY: radian measure measure of an angle in standard position 4. ANS: 300º PTS: 1 DIF: L2 REF: 13-3 Radian Measure OBJ: Using Radian Measure TOP: 13-3 Example 2 KEY: radian measure measure of an angle in standard position 5. ANS: 0.7 PTS: 1 DIF: L2 REF: 13-4 The Sine Function OBJ: Interpreting Sine Functions TOP: 13-4 Example 1 KEY: sine function graphing 6. ANS: 2π PTS: 1 DIF: L2 REF: 13-4 The Sine Function OBJ: Interpreting Sine Functions TOP: 13-4 Example 3 KEY: sine function period graphing 1

8 7. ANS: amplitude = 10, period = π PTS: 1 DIF: L3 REF: 13-4 The Sine Function OBJ: Interpreting Sine Functions TOP: 13-4 Example 4 KEY: amplitude period sine function problem solving word problem 8. ANS: PTS: 1 DIF: L2 REF: 13-4 The Sine Function OBJ: Graphing Sine Functions TOP: 13-4 Example 6 KEY: amplitude graphing sine function period 9. ANS: y = 4 sin 4θ PTS: 1 DIF: L2 REF: 13-4 The Sine Function OBJ: Graphing Sine Functions TOP: 13-4 Example 7 KEY: amplitude graphing period 10. ANS: y = cos θ PTS: 1 DIF: L2 REF: 13-5 The Cosine Function OBJ: Solving Trigonometric Equations TOP: 13-5 Example 3 KEY: amplitude cosine function graphing period 2

9 11. ANS: PTS: 1 DIF: L2 REF: 13-6 The Tangent Function OBJ: Graphing the Tangent Function TOP: 13-6 Example 2 KEY: period graphing tangent function 12. ANS: period = 4 3 ; two asymptotes at x = 2 3 and x = 2 PTS: 1 DIF: L3 REF: 13-6 The Tangent Function OBJ: Graphing the Tangent Function TOP: 13-6 Example 3 KEY: graphing period asymptote tangent function 13. ANS: 1 PTS: 1 DIF: L2 REF: 13-8 Reciprocal Trigonometric Functions OBJ: Evaluating Reciprocal Trigonometric Functions TOP: 13-8 Example 3 KEY: reciprocal trigonometric functions cosecant cotangent secant 14. ANS: 0.03, 1.00 PTS: 1 DIF: L3 REF: 13-2 Angles and the Unit Circle OBJ: Using the Unit Circle TOP: 13-2 Example 3 KEY: cosine of an angle measure of an angle in standard position sine of an angle unit circle 15. ANS: 16.2 feet PTS: 1 DIF: L4 REF: 13-8 Reciprocal Trigonometric Functions OBJ: Graphing Reciprocal Trigonometric Functions TOP: 13-8 Example 6 KEY: reciprocal trigonometric functions graphing calculator problem solving secant 3

10 16. ANS: about 63º PTS: 1 DIF: L4 REF: 13-5 The Cosine Function OBJ: Solving Trigonometric Equations KEY: sine equation cosine equation graphing calculator 17. ANS: 80 feet PTS: 1 DIF: L2 REF: 14-3 Right Triangles and Trigonometric Ratios OBJ: Finding the Lengths of Sides in a Right Triangle TOP: 14-3 Example 1 KEY: trigonometric ratios tangent function angle measure problem solving 18. ANS: ; 0.96 PTS: 1 DIF: L2 REF: 14-3 Right Triangles and Trigonometric Ratios OBJ: Finding the Lengths of Sides in a Right Triangle TOP: 14-3 Example 2 KEY: trigonometric ratios Pythagorean Theorem 19. ANS: 18.7 PTS: 1 DIF: L2 REF: 14-3 Right Triangles and Trigonometric Ratios OBJ: Finding the Lengths of Sides in a Right Triangle TOP: 14-3 Example 3 KEY: angle measure trigonometric ratios tangent function 20. ANS: 3.4 PTS: 1 DIF: L2 REF: 14-3 Right Triangles and Trigonometric Ratios OBJ: Finding the Lengths of Sides in a Right Triangle TOP: 14-3 Example 3 KEY: angle measure trigonometric ratios sine function 21. ANS: 67.6 PTS: 1 DIF: L2 REF: 14-3 Right Triangles and Trigonometric Ratios OBJ: Finding the Measures of Angles in a Right Triangle TOP: 14-3 Example 4 KEY: angle measure trigonometric ratios cosine function 22. ANS: 25.7 cm PTS: 1 DIF: L2 REF: 13-3 Radian Measure OBJ: Finding the Length of an Arc TOP: 13-3 Example 4 KEY: length of an intercepted arc measure of an angle in standard position radian measure 4

11 23. ANS: 1,980.1 in. 2 PTS: 1 DIF: L2 REF: 14-4 Area and the Law of Sines OBJ: Area and the Law of Sines TOP: 14-4 Example 1 KEY: area and the Law of Sines 24. ANS: 61.1 PTS: 1 DIF: L2 REF: 14-4 Area and the Law of Sines OBJ: Area and the Law of Sines TOP: 14-4 Example 2 KEY: Law of Sines 25. ANS: 62.6 PTS: 1 DIF: L2 REF: 14-5 The Law of Cosines OBJ: The Law of Cosines TOP: 14-5 Example 1 KEY: Law of Cosines 5