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Algebra IIA Unit X: Trigonometric Functions • Foundational Material Use inverses of functions Measure indirectly using ratios and proportional reasoning Use of equations of circles on the coordinate plane • Goal Use trigonometric functions and their inverses Measure indirectly using side lengths and angles of triangles Use angles of rotation and find arc lengths of circles • • Why? To have the skill for precalculus and calculus To study in scientific fields such as astronomy, forensics, geology, and engineering Key Vocabulary Angle of Rotation Coterminal Angle Initial side To apply knowledge in navigation, surveying, drafting, architecture, landscaping and aviation Radian Reference angle Standard Position Terminal Side Trigonometric Function Unit Circle Lesson 1: Right Triangle Trigonometry Understand and use trigonometric relationships of acute angles in triangles. Determine side lengths of right triangles by using trigonometric functions. Solve right triangles and special right triangles Find the six trigonometric functions given a right triangle. Solve applications involving right triangles. Use inverse functions to solve trigonometric equations that arise in modeling contexts, evaluate the solutions using technology, and interpret them in terms of the context. (CC.9-12.F.TF.7 (+)) Right Triangles: The 3 Major Trig Functions: 1. 2. 3. How to remember them: _______________________ Example #1: Find the value of the sine, cosine, and tangent functions for θ A. B. The 3 Reciprocal Trig Functions: 4. 5. 6. Example #2: Find the values of the 6 trigonometric functions for θ Trig Ratios in Special Right Triangles: Example #3: Use a trigonometric function to find the value of x A. B. You Try: Use a trigonometric function to find the exact value of each variable 1. 2. Finding a Missing Side: 1. Determine the trig function to use. 2. Plug in the given values. 3. Solve. Example #4: In a waterskiing competition, a jump ramp has the measurements shown. What is the height h above water that a skier leaves the ramp? Angles of Depression & Elevation: 3. Example #5A: A biologist whose eye level is 6 ft above the ground measures the angle of elevation to the top of a tree to be 38.7°. If the biologist is standing 180 ft from the tree’s base, what is the height of the tree to the nearest foot? Example #5B: The pilot of a hot-air balloon measures the angle of depression to a landing spot to be 20.5°. If the pilot’s altitude is 90 m, what is the horizontal distance between the balloon and the landing spot? Homework: p. 697-699 #13-23, 30-32