4.2 Notes – Unit Circle Objectives: You should 1. 2. 3. 4. be able to draw and correctly label the unit circle. be able to use the coordinates of the points on the unit circle to find trig values at a given point. know the domain and period of sine and cosine. be able to use a calculator to evaluate trig expressions. Vocabulary: unit circle, sine, cosine, tangent, cotangent, secant, cosecant, domain, period, periodic Unit circle: the circle given by the equation x2 + y2 = 1 Where is the center of the circle? _____________ What is the largest x-value? __________ smallest? __________ What is the largest y-value? __________ smallest? __________ Unit circle activity (separate page) Definitions of Trigonometric Functions: Let be a real number (specifically an angle measure) and let (x, y) be the point on the unit circle that corresponds to . sin 𝜃 = 𝑦 tan 𝜃 = 𝑦 ,𝑥 ≠ 0 𝑥 sec 𝜃 = 1 ,𝑥 ≠ 0 𝑥 cos 𝜃 = 𝑥 cot 𝜃 = 𝑥 ,𝑦 ≠ 0 𝑦 csc 𝜃 = 1 ,𝑦 ≠ 0 𝑦 Unit circle table (separate page) Use a calculator to evaluate the trig functions. 1. sin 11𝜋 9 2. cos 58° 3. csc −13.4 Assignment: pg. 270 #13-29 eoo, 53-69 odds Angle Measure degrees radians 0 𝜋 6 45 60 90 2𝜋 3 135 150 180 𝜋 210 5𝜋 4 240 3𝜋 2 300 315 330 360 sin cos Trig Function Values tan cot sec csc