III. Solve for the value of x using a scientific calculator and round of your answer to whole number. Ex. \( \tan x=\frac{16}{21} \) SOLUTION: \( \tan x=\frac{16}{21} \quad \rightarrow \) take the inverse of tan. This is usually labeled as \( \tan ^{-1} \) or atan \( x=\tan ^{-1}\left(\frac{16}{21}\right) \quad \rightarrow \) divide 16 by 21 to get the decimal form 0.7619 \( \mathrm{x}=\tan ^{-1}(0.7619) \rightarrow \) type this on your scientific calculator and round off your answer to whole number \( \mathrm{x}=37^{\circ} \) 11. \( \cos x=\frac{4}{5} \) 14. \( \sin x=\frac{12}{17} \) 12. \( \sin x=\frac{2}{5} \) 15. \( \tan x=\frac{13}{25} \) 13. \( \tan x=\frac{7}{5} \) 16. \( \cos x=\frac{8}{15} \)

Below are the steps and answers for each problem. (Remember: When using your scientific calculator, ensure it is in degree mode.) Example:  tan x = 16/21  Step 1. Compute 16 ÷ 21 = 0.7619  Step 2. Find x = tan⁻¹(0.7619) ≈ 37°  Thus, x ≈ 37°. Now for the given problems: 11. cos x = 4/5  • Compute 4 ÷ 5 = 0.8  • Find x = cos⁻¹(0.8) ≈ 36.87°  • Rounding to the nearest whole number gives: x ≈ 37° 12. sin x = 2/5  • Compute 2 ÷ 5 = 0.4  • Find x = sin⁻¹(0.4) ≈ 23.58°  • Rounding to the nearest whole number gives: x ≈ 24° 13. tan x = 7/5  • Compute 7 ÷ 5 = 1.4  • Find x = tan⁻¹(1.4) ≈ 54.46°  • Rounding to the nearest whole number gives: x ≈ 54° 14. sin x = 12/17  • Compute 12 ÷ 17 ≈ 0.7059  • Find x = sin⁻¹(0.7059) ≈ 45°  • Rounding gives: x ≈ 45° 15. tan x = 13/25  • Compute 13 ÷ 25 = 0.52  • Find x = tan⁻¹(0.52) ≈ 27.32°  • Rounding to the nearest whole number gives: x ≈ 27° 16. cos x = 8/15  • Compute 8 ÷ 15 ≈ 0.5333  • Find x = cos⁻¹(0.5333) ≈ 57.7°  • Rounding to the nearest whole number gives: x ≈ 58° Thus, the final rounded answers are: 11. 37°  12. 24°  13. 54°  14. 45°  15. 27°  16. 58°