use the unit circle to find the exact value of each of the following. 1. sin\\(\\frac{3\\pi}{2}\\) 2…

use the unit circle to find the exact value of each of the following. 1. sin\\(\\frac{3\\pi}{2}\\) 2. csc\\(\\frac{7\\pi}{4}\\) =\\(\\frac{2}{\\sqrt{2}}=\\sqrt{2}\\) 3. tan\\(\\frac{\\pi}{3}\\) 4. sec\\(\\left(-\\frac{5\\pi}{6}\\right)\\) 5. cot\\(\\left(-\\frac{11\\pi}{6}\\right)\\) 6. cos\\(\\left(-\\frac{\\pi}{3}\\right)\\) 7. csc\\(\\frac{26\\pi}{3}\\) 8. tan\\(\\left(-\\frac{10\\pi}{3}\\right)\\) 9. sec\\(\\frac{19\\pi}{4}\\) 10. cos\\((-225^{\\circ})\\) 11. cos 0 12. sec\\((-780^{\\circ})\\) 13. csc\\(\\frac{2\\pi}{3}\\) 14. cot\\(\\frac{4\\pi}{3}\\) 15. sin\\((-480^{\\circ})\\) 16. cos\\(\\left(-\\frac{13\\pi}{4}\\right)\\) 17. sin\\(\\frac{47\\pi}{6}\\) 18. sec 900^{\\circ}

use the unit circle to find the exact value of each of the following. 1. sin\\(\\frac{3\\pi}{2}\\) 2. csc\\(\\frac{7\\pi}{4}\\) =\\(\\frac{2}{\\sqrt{2}}=\\sqrt{2}\\) 3. tan\\(\\frac{\\pi}{3}\\) 4. sec\\(\\left(-\\frac{5\\pi}{6}\\right)\\) 5. cot\\(\\left(-\\frac{11\\pi}{6}\\right)\\) 6. cos\\(\\left(-\\frac{\\pi}{3}\\right)\\) 7. csc\\(\\frac{26\\pi}{3}\\) 8. tan\\(\\left(-\\frac{10\\pi}{3}\\right)\\) 9. sec\\(\\frac{19\\pi}{4}\\) 10. cos\\((-225^{\\circ})\\) 11. cos 0 12. sec\\((-780^{\\circ})\\) 13. csc\\(\\frac{2\\pi}{3}\\) 14. cot\\(\\frac{4\\pi}{3}\\) 15. sin\\((-480^{\\circ})\\) 16. cos\\(\\left(-\\frac{13\\pi}{4}\\right)\\) 17. sin\\(\\frac{47\\pi}{6}\\) 18. sec 900^{\\circ}

Answer

Explanation:

Step1: Find the reference angle

For (\cos(-225^{\circ})), use the property (\cos(-\theta)=\cos\theta), so (\cos(-225^{\circ})=\cos225^{\circ}). (225^{\circ}=180^{\circ} + 45^{\circ}), the reference angle (\theta'=225^{\circ}-180^{\circ}=45^{\circ}). Since (225^{\circ}) is in the third - quadrant and (\cos\theta) is negative in the third - quadrant.

Step2: Calculate the value

(\cos225^{\circ}=-\cos45^{\circ}). We know that (\cos45^{\circ}=\frac{\sqrt{2}}{2}), so (\cos(-225^{\circ})=-\frac{\sqrt{2}}{2}).

Answer:

(-\frac{\sqrt{2}}{2})