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Section 4-1 What we know. Click on any that apply to be true about right triangles. 0%A. Right triangles have a 180 degrees in them 0% B. Right triangles have a 90 degree angle C. Trigonometry can be used on any type of triangle. 0% D. There are 4 main trigonometric functions. 0%E. There is only one way to always look at any of these 0% problems. Vocabulary Trigonometry: The study of relationships among the angles and sides of a right triangle. Trigonometric ratio: compares the sides lengths of a right triangle. Trigonometric Functions: has a rules given by a trigonometric ratio A. Sine B. Main C. Cosine Choose the six basic trigonometric Functions. Choose any that apply. D. Tangent 0% E. Peroant F. Cosecant G. Secant H. Cotangent I. Gauss J. Cosme Sine Main Cosine Tangent Peroant Gauss Cosecant Cosme Secant Cotangent 60 Countdown Trig Functions of Right Triangles Sine (sin)θ = 𝑜𝑝𝑝 ℎ𝑦𝑝 Cosine (cos)θ = Cosecant (csc)θ = 𝑎𝑑𝑗 ℎ𝑦𝑝 Tangent (tan)θ = 𝑜𝑝𝑝 𝑎𝑑𝑗 Secant (sec)θ = ℎ𝑦𝑝 𝑜𝑝𝑝 ℎ𝑦𝑝 𝑎𝑑𝑗 Cotangent (cot)θ = 𝑎𝑑𝑗 𝑜𝑝𝑝 Evaluate the six trigonometric functions. 17 8 𝜃 15 Special Triangles 600 450 2x x 𝑥 2 x 300 x 3 450 x Find the missing side length 10 8 x x 300 450 Inverse Trig Functions Allows us to know side lengths and find missing angles. Have all six trig functions still sin−1 1 sin−1 , cos −1 = csc −1 , tan−1 , 1 cos−1 = sec −1 , and 1 tan−1 = cot −1 Place the six trig functions with their correct association. a = sin, b = cos, c = tan, d = csc, e = sec, f = cot. 𝑜𝑝𝑝 ℎ𝑦𝑝 ℎ𝑦𝑝 𝑜𝑝𝑝 𝑎𝑑𝑗 𝑎𝑑𝑗 1= ,2 = ,3 = ,4 = , 5 = 𝑜𝑝𝑝 , 6 = ℎ𝑦𝑝 , ℎ𝑦𝑝 𝑎𝑑𝑗 𝑜𝑝𝑝 𝑎𝑑𝑗 A. a1,b6, c2, d3, e5, f4 0% B. a1, b6, c4, d2, e4, f5 C. a1, b6, c5, d2, e3, f4, D. a1, b6, c4, d3,e2, f5 E. a1, b6, c2, d5, e4, f3 a1,b6, c2, d3, e5... a1, b6, c4, d2, e... a1, b6, c4, d3,e... a1, b6, c2, d5, e... a1, b6, c5, d2, e... 180 Countdown A hot air balloon that is moving above a neighborhood has an angle of depression of 28 degrees to on house and 52 degrees to a house down the street. If the height of the balloon is 650 ft, estimate the distance between the two houses. Determine your comfort level with the material so far… A. I got this! B. I have about 75% of 0% this! C. I am getting there! D. I am lost! I got this! I have about 75% ... I am getting there! I am lost! 10 Countdown Homework Section 4-1 pg 227 4, 28, 30, 39, 42, 43, 45, 57-68