Trigonometry (11th Edition)
Trigonometry (11th Edition)
11th Edition
ISBN: 9780134217437
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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**Trigonometry Exercises and Identities** **Exercises 37-40:** - Find the terminal side of an angle \(\theta\) on the line in the given quadrant. - Calculate the six trigonometric functions of \(\theta\). - Compare the slope of the line to \(\tan \theta\). 37. \(y = -4x\), Quadrant II 38. \(y = \frac{1}{2}x\), Quadrant I 39. \(y = 6x\), Quadrant III 40. \(y = \frac{3}{2}x\), Quadrant IV **Exercises 41-48: Critical Thinking** - If the given angle is in standard position, determine the slope \(m\) of the angle's terminal side. - Approximate your answer to two decimals where appropriate. 41. \(45^\circ\) 42. \(135^\circ\) 43. \(-240^\circ\) 44. \(-150^\circ\) 45. \(65^\circ\) 46. \(187^\circ\) 47. \(-310^\circ\) 48. \(-110^\circ\) **Identities** **Exercises 49-58:** - Determine the values of the trigonometric functions of \(\theta\) using the given information. 49. \(\sin \theta = \frac{3}{5}\) and \(\cos \theta = \frac{4}{5}\) 50. \(\sin \theta = \frac{-7}{25}\) and \(\cos \theta = \frac{24}{25}\) 51. \(\csc \theta = \frac{17}{15}\) and \(\sec \theta = \frac{-17}{8}\) 52. \(\csc \theta = 2\) and \(\sec \theta = \frac{-2}{\sqrt{3}}\) 53. \(\tan \theta = \frac{5}{12}\) and \(\cos \theta = \frac{12}{13}\) **(Hint: \(\sin \theta = \tan \theta \cos \theta\))** 54. \(\sin \theta = \frac{3}{5}\) and \(\cot \theta = \frac{-4}{3}\) 55. \(\sin
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Transcribed Image Text:**Trigonometry Exercises and Identities** **Exercises 37-40:** - Find the terminal side of an angle \(\theta\) on the line in the given quadrant. - Calculate the six trigonometric functions of \(\theta\). - Compare the slope of the line to \(\tan \theta\). 37. \(y = -4x\), Quadrant II 38. \(y = \frac{1}{2}x\), Quadrant I 39. \(y = 6x\), Quadrant III 40. \(y = \frac{3}{2}x\), Quadrant IV **Exercises 41-48: Critical Thinking** - If the given angle is in standard position, determine the slope \(m\) of the angle's terminal side. - Approximate your answer to two decimals where appropriate. 41. \(45^\circ\) 42. \(135^\circ\) 43. \(-240^\circ\) 44. \(-150^\circ\) 45. \(65^\circ\) 46. \(187^\circ\) 47. \(-310^\circ\) 48. \(-110^\circ\) **Identities** **Exercises 49-58:** - Determine the values of the trigonometric functions of \(\theta\) using the given information. 49. \(\sin \theta = \frac{3}{5}\) and \(\cos \theta = \frac{4}{5}\) 50. \(\sin \theta = \frac{-7}{25}\) and \(\cos \theta = \frac{24}{25}\) 51. \(\csc \theta = \frac{17}{15}\) and \(\sec \theta = \frac{-17}{8}\) 52. \(\csc \theta = 2\) and \(\sec \theta = \frac{-2}{\sqrt{3}}\) 53. \(\tan \theta = \frac{5}{12}\) and \(\cos \theta = \frac{12}{13}\) **(Hint: \(\sin \theta = \tan \theta \cos \theta\))** 54. \(\sin \theta = \frac{3}{5}\) and \(\cot \theta = \frac{-4}{3}\) 55. \(\sin
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Step 1: Given

Given that 

sin theta equals negative 12 over 13 cos theta less than 0

The aim is to find the value of theta


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