2. a. Use Ptolemy's known chords from the reading (or from videos) and the half-angle chord identity to find the chords of the following angles: 30° and 45°. You may answer this one with a decimal approximation. Do not use sine and cosine or the chord table. b. Use Ptolemy's known chords from the reading (or from videos) and the supplementary angle chord formula to find the and the chord of 108°. You may answer this one with a decimal approximation. Do not use sine and cosine or the chord table. c. Use Ptolemy's known chords from the reading (or from class notes) and the chord sum formula (from class notes) to find the chord of 12°. You may answer this one with a decimal approximation. Do not use sine and cosine or the chord table. d. We wish to compare Ptolemy's chords with some known sines, namely sin 30°, sin 45°, and sin 60°. i. Convert sin 30°, sin 45°, and sin 60° to chords. ii. Compute the decimal approximations of these chords using the known chords from the reading (or from videos). iii. Compare with the decimal approximations of the exact values of sin 30°, sin 45°, and sin 60° that we know from high school.