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Warm Up 1. Given the following trig value, sketch a triangle and find the remaining 5 ratios. Mar. st 31 2. Use Pythagorean theorem to solve for x then find all six trig ratios for θ. csc 3 3. Convert 150○ to radians. 4. Convert 5π/4 to degrees. Homework Check & Questions? • 1. Quick Review or Right Triangle Trig & Angle Measures Building & Using The Unit Circle Examples • Let (6, 8) be a point on the terminal side of . Find all six trig ratios. Examples (cont.) • Let (-5, -12) be a point on the terminal side of . Find all six trig ratios. Examples (cont.) • Find the values of the 6 trig functions of . 2 tan and lies in quadrant IV 5 What quadrant are you in if… cos 0 and csc 0 sin 0 and tan 0 sec 0 and cot 0 • Standard Position • Positive and Negative Angles • Wrapping Angles Degrees, Minutes, Seconds… 1) Change 25.36○ to degrees, minutes, seconds. 2) Change -175○ 30’ 45” to decimal degrees. Angles… Determine the quadrant in which the terminal side of the angle lies and sketch the angle in standard position. 1) 100○ 2) -290○50’ 3) 9π/5 4) -2.5 Coterminal Angles… • Determine two coterminal angles (one negative and one positive) for each given angle. 1) 140○ 2) 3π/7 Use Geometry to determine the exact value of the missing side length of each special right triangle. Complete the first quadrant of the Unit Circle A reference angle is the acute angle formed by the terminal side of an angle in standard position and the x-axis. What is the reference angle for … 310º -210º 3π/4 11π/7 Complete the angles (in radians & degrees) the Unit Circle The Unit Circle Using the Unit Circle Find the point on the unit circle that corresponds to the angle. 1) -120○ 2) 495○ 3) -30 ○ 5 4) 6 13 5) 3 3 6) 2 Practice Evaluate each of the following. 7)cos (150 ○) 17 10) sin 6 8) sin (360 ○) 2 11) sin 3 11 9) cos 6 5 12) sin 4 Trig Functions (and their relationship to sine/cosine) tan cot sec csc sin cos cos 1 or sin tan 1 (flip over the cos) cos 1 (flip over the sin) sin More Practice Evaluate each of the following. 1. tan(240○) 2. csc(-225○) 3) cot(20π/3) 4) sec(- π/4) Examples (cont.) • Let (-4, 0) be a point on the terminal side of . Find all six trig ratios. • Let (0, 9) be a point on the terminal side of . Find all six trig ratios. Extra Practice Find all 6 trig ratios from the given information. 1. 2. sinθ = 8/13 4. (6, -6) 18 14 3. cotθ = 5 5. (-1, -2) 6. cosθ = -1/2, where θ lies in Quadrant II More Extra Practice • No calculator… 1. Determine the reference angle. 7 a) -100○ b) 10 2. Determine the quadrant in which the angle lies. 31 ○ a) -2.15 b) 300 c) 12 Determine two coterminal angles (one pos., one neg.) 2 a) b) 700○ 3 Even More Extra Practice Evaluate each of the following. 1) cos (150 ○) 17 4) sin 6 2) sin (360 ○) 11 3) cos 6 2 5) sin 3 5 6) sin 4 7) tan(240○) 8) csc(-225○) 9) cot(20π/3) 10) sec(- π/4)