We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

Study Guides > Precalculus II

Solutions for the Other Trigonometric Functions

Solutions to Try Its

1. sin⁡t=−22,cos⁡t=22,tan⁡t=−1,sec⁡t=2,csc⁡t=−2,cot⁡t=−1\sin t=-\frac{\sqrt{2}}{2},\cos t=\frac{\sqrt{2}}{2},\tan t=-1,\sec t=\sqrt{2},\csc t=-\sqrt{2},\cot t=-1 2. sin⁡π3=32cos⁡π3=12tan⁡π3=3sec⁡π3=2csc⁡π3=233cot⁡π3=33\begin{array}{l}\sin \frac{\pi }{3}=\frac{\sqrt{3}}{2}\\ \cos \frac{\pi }{3}=\frac{1}{2}\\ \tan \frac{\pi }{3}=\sqrt{3}\\ \sec \frac{\pi }{3}=2\\ \csc \frac{\pi }{3}=\frac{2\sqrt{3}}{3}\\ \cot \frac{\pi }{3}=\frac{\sqrt{3}}{3}\end{array} 3. sin⁡(−7π4)=22,cos⁡(−7π4)=22,tan⁡(−7π4)=1\sin \left(\frac{-7\pi }{4}\right)=\frac{\sqrt{2}}{2},\cos \left(\frac{-7\pi }{4}\right)=\frac{\sqrt{2}}{2},\tan \left(\frac{-7\pi }{4}\right)=1, sec⁡(−7π4)=2,csc⁡(−7π4)=2,cot⁡(−7π4)=1\sec \left(\frac{-7\pi }{4}\right)=\sqrt{2},\csc \left(\frac{-7\pi }{4}\right)=\sqrt{2},\cot \left(\frac{-7\pi }{4}\right)=1 4. −3-\sqrt{3} 5. −2-2 6. sin⁡t\sin t 7. cos⁡t=−817,sin⁡t=1517,tan⁡t=−158\cos t=-\frac{8}{17},\sin t=\frac{15}{17},\tan t=-\frac{15}{8} csc⁡t=1715,cot⁡t=−815\csc t=\frac{17}{15},\cot t=-\frac{8}{15} 8. sin⁡t=−1,cos⁡t=0,tan⁡t=Undefinedsec⁡t=Undefined,csc⁡t=−1,cot⁡t=0\begin{array}{l}\sin t=-1,\cos t=0,\tan t=\text{Undefined}\\ \sec t=\text{\hspace{0.17em}Undefined,}\csc t=-1,\cot t=0\end{array} 9. sec⁡t=2,csc⁡t=2,tan⁡t=1,cot⁡t=1\sec t=\sqrt{2},\csc t=\sqrt{2},\tan t=1,\cot t=1 10. ≈−2.414\approx -2.414

Solutions to Odd-Numbered Exercises

1. Yes, when the reference angle is π4\frac{\pi }{4} and the terminal side of the angle is in quadrants I and III. Thus, at x=π4,5π4x=\frac{\pi }{4},\frac{5\pi }{4}, the sine and cosine values are equal. 3. Substitute the sine of the angle in for yy in the Pythagorean Theorem x2+y2=1{x}^{2}+{y}^{2}=1. Solve for xx and take the negative solution. 5. The outputs of tangent and cotangent will repeat every π\pi  units. 7. 233\frac{2\sqrt{3}}{3} 9. 3\sqrt{3} 11. 2\sqrt{2} 13. 1 15. 2 17. 33\frac{\sqrt{3}}{3} 19. −233-\frac{2\sqrt{3}}{3} 21. 3\sqrt{3} 23. −2-\sqrt{2} 25. −1 27. −2 29. −33-\frac{\sqrt{3}}{3} 31. 2 33. 33\frac{\sqrt{3}}{3} 35. −2 37. −1 39. If sin⁡t=−223,sec⁡t=−3,csc⁡t=−324,tan⁡t=22,cot⁡t=24\sin t=-\frac{2\sqrt{2}}{3},\sec t=-3,\csc t=-\frac{3\sqrt{2}}{4},\tan t=2\sqrt{2},\cot t=\frac{\sqrt{2}}{4} 41. sec⁡t=2,csc⁡t=233,tan⁡t=3,cot⁡t=33\sec t=2,\csc t=\frac{2\sqrt{3}}{3},\tan t=\sqrt{3},\cot t=\frac{\sqrt{3}}{3} 43. −22-\frac{\sqrt{2}}{2} 45. 3.1 47. 1.4 49. sin⁡t=22,cos⁡t=22,tan⁡t=1,cot⁡t=1,sec⁡t=2,csc⁡t=2\sin t=\frac{\sqrt{2}}{2},\cos t=\frac{\sqrt{2}}{2},\tan t=1,\cot t=1,\sec t=\sqrt{2},\csc t=\sqrt{2} 51. sin⁡t=−32,cos⁡t=−12,tan⁡t=3,cot⁡t=33,sec⁡t=−2,csc⁡t=−233\sin t=-\frac{\sqrt{3}}{2},\cos t=-\frac{1}{2},\tan t=\sqrt{3},\cot t=\frac{\sqrt{3}}{3},\sec t=-2,\csc t=-\frac{2\sqrt{3}}{3} 53. –0.228 55. –2.414 57. 1.414 59. 1.540 61. 1.556 63. sin⁡(t)≈0.79\sin \left(t\right)\approx 0.79 65. csc⁡t≈1.16\csc t\approx 1.16 67. even 69. even 71. sin⁡tcos⁡t=tan⁡t\frac{\sin t}{\cos t}=\tan t 73. 13.77 hours, period: 1000π1000\pi 75. 7.73 inches

Licenses & Attributions