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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. 5 sin 13 12 cos 13 5 tan 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. 2 29 sin 29 5 29 cos 29 2 tan 5 Example 3 Given the following, find the 6 trigonometric ratios: sec Θ = -2 sin Θ > 0 3 sin 2 1 cos 2 tan 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 α = 51o α = 2 5 1 3 3 2 5 3 1 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 510o 1 2 3 2 3 tan 510o 3 cos 510o csc 510o 2 2 3 sec 510 3 cot 510o 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 11 sin 4 11 cos 4 11 tan 1 4 4 2 2 2 2 11 csc 2 4 11 sec 2 4 11 cot 1 4 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. 3 Given: sin 2 Θ