In this module you have worked with many different trigonometric identities. These identities can be helpful for making precise calculations. For example, you can use identities to find the lengths of the sides of a triangle when the angle measure in standard position is not listed on the unit circle. Most recently you have learned about double-angle and half-angle identities. These are special cases of the sum and difference formulas for sine and cosine. Consider the half-angle identities shown as you work through the scenario below. Sine Half-Angle Identity Cosine Half-Angle Identity 1- cose 0 sin = ± 1+ cose Ꮎ cos = ± 2 2 Marcus is a craftsman and artist. He uses the knowledge he has gained as an engineering student to create custom pieces. For his current project, he is making a large, intricate, 3-dimensional latticework that will be placed next to the marker which welcomes people to his city. He has the work on the lattice completed. It consists of two long rectangles, such that the bottom rectangle will act as a base for the top rectangle. Together the two rectangles are 12 feet tall. 12 ft In order to help the latticework remain vertical, Marcus will attach two wires to each side of the piece, and affix them to the ground at a point that is exactly 9 feet from the base of the artwork, as shown in the illustration. The measure of the angle of elevation to the top of the base is one-half the measure of the angle of elevation to the top of the latticework. Use this information and what you know about trigonometric ratios and identities to help you explore the questions below. 9 ft