Use your calculator to determine the following: \( \begin{array}{ll}\text { 1. } \sin 213^{\circ} & \text { 2. } \cos 205^{\circ} \\ \text { 3. } \tan 57,13^{\circ} & \text { 4. } \cot 115^{\circ} 25^{\prime} \\ \text { 5. } \sec 304,4^{\circ} & \text { 6. } \operatorname{cosec} 97^{\circ} 12^{\prime} 14^{\prime \prime} \\ \text { 7. } \sin ^{-1}(0,213) & \text { 8. } \cos ^{-1}(-0,432) \\ \text { 9. } \tan ^{-1}(1,73) & \text { 10. } \cot ^{-1}(-0,462) \\ \text { 11. } \sec ^{-1}(-2,41) & \text { 12. } \operatorname{cosec}^{-1}(3,21)\end{array} \)

Alright, I need to calculate the values of these trigonometric functions using a calculator. Let's go through each one step by step. 1. **sin 213°** - 213 degrees is in the third quadrant where sine is negative. - sin(213°) = sin(180° + 33°) = -sin(33°) - Calculating sin(33°) ≈ 0.5446 - Therefore, sin(213°) ≈ -0.5446 2. **cos 205°** - 205 degrees is in the third quadrant where cosine is negative. - cos(205°) = cos(180° + 25°) = -cos(25°) - Calculating cos(25°) ≈ 0.9063 - Therefore, cos(205°) ≈ -0.9063 3. **tan 57,13°** - 57.13 degrees is in the first quadrant where tangent is positive. - tan(57.13°) = sin(57.13°) / cos(57.13°) - Calculating sin(57.13°) ≈ 0.8409 - Calculating cos(57.13°) ≈ 0.5403 - Therefore, tan(57.13°) ≈ 0.8409 / 0.5403 ≈ 1.555 4. **cot 115° 25'** - 115 degrees and 25 minutes is in the second quadrant where cotangent is negative. - First, convert 25 minutes to degrees: 25' = 25/60 ≈ 0.4167° - So, 115° 25' ≈ 115.4167° - cot(115.4167°) = 1 / tan(115.4167°) - Calculating tan(115.4167°) ≈ -0.4663 - Therefore, cot(115.4167°) ≈ 1 / (-0.4663) ≈ -2.147 5. **sec 304,4°** - 304.4 degrees is in the fourth quadrant where secant is positive. - sec(304.4°) = 1 / cos(304.4°) - Calculating cos(304.4°) ≈ 0.5878 - Therefore, sec(304.4°) ≈ 1 / 0.5878 ≈ 1.701 6. **cosec 97° 12' 14'** - 97 degrees, 12 minutes, and 14 seconds is in the first quadrant where cosecant is positive. - First, convert 12 minutes and 14 seconds to degrees: - 12' = 12/60 = 0.2° - 14" = 14/3600 ≈ 0.003889° - So, 97° 12' 14" ≈ 97.203889° - cosec(97.203889°) = 1 / sin(97.203889°) - Calculating sin(97.203889°) ≈ 0.9925 - Therefore, cosec(97.203889°) ≈ 1 / 0.9925 ≈ 1.0075 7. **sin⁻¹(0.213)** - The inverse sine of 0.213. - sin⁻¹(0.213) ≈ 12.3° 8. **cos⁻¹(-0.432)** - The inverse cosine of -0.432. - cos⁻¹(-0.432) ≈ 114.5° 9. **tan⁻¹(1.73)** - The inverse tangent of 1.73. - tan⁻¹(1.73) ≈ 60° 10. **cot⁻¹(-0.462)** - The inverse cotangent of -0.462. - cot⁻¹(-0.462) ≈ 113.5° 11. **sec⁻¹(-2.41)** - The inverse secant of -2.41. - sec⁻¹(-2.41) ≈ 104.5° 12. **cosec⁻¹(3.21)** - The inverse cosecant of 3.21. - cosec⁻¹(3.21) ≈ 18.5°