TRIGONOMETRIC RATIOS AND THE UNIT CIRCLE Mrs. White Precalculus 5.2/5.4 Schedule Class/Week Topic Class Work Homework Mon 2/3 The Unit Circle 5.2 Complete the Unit Circle Template Pg 361 # 3 -30 Multiples of 3 Tues 2/4 Exact Values of the Trig Ratios Examples/Notes Pg. 383 # 3, 14, 18, 22, 34, 39, 43, 54 Wed 2/5 Exact Values of the Trig Ratios Review and Practice Worksheet 5.2 (No calculator) Study for Quiz 5.2 Thurs 2/6 Exact Values of the Trig Ratios Quiz (No Calculator) Watch Video on Graphs of Sine/Cosine Fri 2/7 Trig Ratios and the Unit Circle Goals Students should be able to calculate the exact value of the 6 trigonometric ratios. Review – Complete the Table Θ (degrees) 0o 30o 45o 60o 90o Θ (radians) 0 π/6 π/4 π/3 π/2 sin Θ 0 1 cos Θ 1 0 tan Θ 0 csc Θ Undefined 1 sec Θ 1 Undefined cot Θ Undefined 0 1 Undefined Example 1 Plot P (-12, -5) in the coordinate plane. If the terminal side of an angle in standard position passes through P, find the 6 trig. Ratios. sin 5 13 co s 12 13 ta n 5 12 Example 2 Plot P (5, -2) in the coordinate plane. If the terminal side of an angle in standard position passes through P, find the 6 trig. Ratios. sin 2 29 29 co s 5 29 29 ta n 2 5 Example 3 Given the following, find the 6 trigonometric ratios: sec Θ = -2 sin Θ > 0 sin co s 3 2 1 2 ta n 3 Example 4 Find the reference angle, α. Given: Θ = 309o Find the reference angle, α. Given: Θ = 11 3 α = 360o - 309o Θ = 11 3 α = 51o 2 1 5 3 α = 2 5 1 3 3 Example 5 Evaluate the 6 trig functions of the following angles. No Calculator. Θ = 510° This is coterminal with: 150° Reference angle: 30°, Quadrant 2 sin 5 1 0 o 1 csc 510 2 o 2 co s 5 1 0 o 3 2 tan 5 1 0 o 3 3 sec 510 o 2 3 3 cot 510 3 o Example 6 Evaluate the 6 trig functions of the following angles. No Calculator. 11 Θ= 4 3 This is coterminal with: 4 Reference angle: , Quadrant 3 sin 1 1 4 4 co s tan 1 1 4 1 1 4 2 csc 2 2 sec 2 1 cot 11 4 11 4 11 4 2 2 1 Example 7 Sketch a right triangle corresponding to the trig function of the acute angle, Θ. Find the length of the missing side (using Pythagorean Th). Evaluate the remaining 5 trig. functions at Θ. Given: sin 3 2 Θ