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TRIGONOMETRY REVIEW ANSWERS 5 2 , is on a unit circle. Find the coordinates of its reflection across 1. The point 3 3 the origin, the x-axis, and the y-axis. Answer: 5 2 5 2 5 2 , ; the x-axis: , the origin: , ; the y-axis: 3 3 3 3 3 3 5 11 , and 2. On a unit circle, mark and label the points determined by , , 6 3 2 4 Answer: 3. Sketch a graph of y cos x Answer: 4. What is the range of cosine function? Answer: [-1, 1] 5. What is the period of the sine function? Answer: 2 6. What is the domain of the sine function? Answer: all reals 7. What is the amplitude of the cosine function? Answer: 1 8. Complete the following table: Answer: x sin x cos x 3 3 2 1 2 7 4 2 2 2 2 3 2 1 0 9. Sketch a graph of the tangent function. Answer: 10. What is the period of the tangent function? Answer: 11. What is the domain of the tangent function? Answer: all reals except x n 2 12. What is the range of the tangent function? Answer: all reals 13. In which quadrants are the signs of the tangent and cosecant alike? Answer: I and IV 14. For the angles of the following measures, state in which quadrant the terminal side lies, and convert to radian measure in terms of : a) 210 o b) 54 o c) 225 o Answer: 7 a) II, 6 3 b) I, 10 5 c) III, 4 15. Convert to degree measure: 9 a) 4 b) 3 radians Answer: a) 405 o b) 171.89 o 5 16. Find the length of an arc of a circle, given a central angle of and a radius of 8 6 centimeters. Answer: 20.94 cms 17. A wheel with a 14-cm diameter is rotating at a speed of 10 revolutions per second. What is the velocity, in cm/sec of a point on the rim.? Answer: 440 cms/sec 18. Find the six trigonometric function values for the angle shown: -6 -5 Answer: sin 5 61 , cos 6 61 , tan 61 61 5 6 , csc , sec , cot 6 5 5 6 19. Find the following exactly: a) tan 480 o b) sin( 120 o ) c) cos( 240 o ) Answer: a) 3 3 2 1 c) 2 b) 1 and that the terminal side is in quadrant II, find the other five 3 trigonometric function values. Answer: 2 2 3 3 2 cos , tan , csc 3 , sec , cot 2 2 3 4 4 20. Given that sin 21. Convert 28.35 o to degrees and minutes Answer: 28 o 21 , 22. Convert 89 o 36 to degrees. Answer: 89.6 o 23. Use a calculator to find each of the following: a) sin( 153o 15 17 ) b) cos(1.115) 17 ) c) tan( 3 d) sec(19 o 15 ) e) csc(3.5124) f) cot(1573o ) Answer: a) –0.450025 b) 0.440177 c) 1.73205 d) 1.05922 e) –2.75963 f) –0.932515 24. Use a calculator to find the acute angle that is a solution of the equation. Give the answer in radians: a) cos 0.5324 b) csc 2.1538 Answer: a) 1.0094 b) 0.4828 25. Use a calculator to find in the interval indicated: a) sin 0.5932, (90 o ,180 o ) b) tan 5.321, ( , ) 2 2 Answer: a) 143.62 degrees b) –1.3850 radians 26. Sketch the graph of y 2 sin( x ) . Answer: 27. What is the period of the function in Question 26? Answer: 2 28. What is the phase shift of the function in Question 26? Answer: 1 29. A point on the unit circle has an x-coordinate of . What is the y-coordinate? 4 15 Answer: 4 30. Solve the following equations, if possible: a) 8 cos x 10 b) 2 sin 2 sin 1 c) tan 2 5 tan 3 0 Answer: a) No solution 7 11 , , b) 2 6 6 c) 1.7992, 2.5327, 4.9407