4-3 Trigonometric Functions on the Unit Circle
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1 Find the exact value of each trigonometric function, if defined. If not defined, write undefined. 9. sin The terminal side of in standard position lies on the positive y-axis. Choose a point P(0, 1) on the 13. cos ( 270 ) The terminal side of in standard position lies on the positive y-axis. Choose a point P(0, 1) on the 14. sec tan 2π The terminal side of in standard position lies on the positive x-axis. Choose a point P(1, 0) on the The terminal side of in standard position lies on the negative x-axis. Choose a point P(, 0) on the 15. tan π 11. cot ( 180 ) The terminal side of in standard position lies on the negative x-axis. Choose a point P(, 0) on the The terminal side of π in standard position lies on the negative x-axis. Choose a point P(, 0) on the csc 270 The terminal side of in standard position lies on the negative y-axis. Choose a point P(0, ) on the The terminal side of in standard position lies on the negative y-axis. Choose a point P(0, ) on the esolutions Manual - Powered by Cognero Page 1
2 Sketch each angle. Then find its reference angle The terminal side of 210º lies in Quadrant III. Therefore, its reference angle is θ ' = 210º 180º or 30º. 19. The terminal side of lies in Quadrant II. Therefore, its reference angle is θ ' = The terminal side of 135º lies in Quadrant II. Therefore, its reference angle is θ ' = 180º 135º or 45º. 20. A coterminal angle is 2π or, which lies in Quadrant IV. So, the reference angle is θ ' is 2π or. esolutions Manual - Powered by Cognero Page 2
3 A coterminal angle is (2) or 315. The terminal side of 315 lies in Quadrant IV, so its reference angle is 360º 315º or 45º. 24. A coterminal angle is + 2( 1)π or The terminal side of lies in Quadrant I, so the reference angle is A coterminal angle is or 285. The terminal side of 285 lies in Quadrant IV, so its reference angle is or 75. Find the exact value of each expression. 25. cos Because the terminal side of θ lies in Quadrant III, the reference angle θ ' is π or. 23. The terminal side of lies in Quadrant II. Therefore, its reference angle is θ ' =. In Quadrant III, cos θ is negative and esolutions Manual - Powered by Cognero Page 3
4 26. tan Because the terminal side of θ lies in Quadrant III, the reference angle θ ' is or. 28. cot ( 45 ) A coterminal angle is or 315. Because the terminal side of 315 lies in Quadrant IV, the reference angle θ ' is or 45. Because tangent and cotangent are reciprocal functions and tan θ is negative in Quadrant IV, it follows that cot θ is also negative in Quadrant IV. In Quadrant III, tan θ is positive and. 27. sin Because the terminal side of θ lies in Quadrant II, the reference angle θ ' is or. In Quadrant II, sin θ is positive and. esolutions Manual - Powered by Cognero Page 4
5 29. csc 390 A coterminal angle is or 30, which lies in Quadrant I. So, the reference angle θ ' is or 30. Because sine and cosecant are reciprocal functions and sin θ is positive in Quadrant I, it follows that csc θ is also positive in Quadrant I. 30. sec ( 150 ) A coterminal angle is or 210, which lies in Quadrant III. Because the terminal side of θ lies in Quadrant III. So, the reference angle θ ' is 210º 180º or 30º. Because secant and cosine are reciprocal functions and cos θ is negative in Quadrant III, it follows that sec θ is also negative in Quadrant III. esolutions Manual - Powered by Cognero Page 5
6 31. tan Because the terminal side of θ lies in Quadrant IV, 32. sin 300 Because the terminal side of θ lies in Quadrant IV, the reference angle θ ' is or. the reference angle θ ' is or. In Quadrant IV, tan θ is negative. In Quadrant IV, sin θ is negative. esolutions Manual - Powered by Cognero Page 6
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