2) Find one positive and one negative coterminal angle to 𝜋 3 . Warm-up: 1) r = 9, θ = 230º 2) Find one positive and one negative coterminal angle to 𝜋 3 . Find arc length S. HW: Pg377- 8 (2 – 30 even, 33, 37, 39, 41, 45, 47, 51) Timed Five Minute Quiz on Unit Circle tomorrow!

a. I b.III a.III b. IV a. IV b. II a. IV b. III a. III b. II HW Answers: p367-368 (5 – 10 , 15 -18 , 25, 27, 33 – 36 , 43 – 61 odd, 71, 73) a. I b.III a.III b. IV a. IV b. II a. IV b. III a. III b. II 15) a. 25/12, -23/12 b. 8/3, -4/3 16) a. 19/6, -5/6 b. /6, -23/6 17) a. 7/4, - /4 b. 28/15, -32/15 18) a.26/9, -10/9 b. 98/45, -82/45 25) a. II b. IV 27) a. III b. I 33) a.405° , -315° b.324°, -396° 34) a.480°, -240 ° b. 330°, -30° 35) a. 660°, -60° b. 20°, -340° 36) a. 300°, -60° b. -130°, 590° 43) a. 270° b.210° 45) a. 420° b. -66°

HW Answers: p367-368 (5 – 10 , 15 -18 , 25, 27, 33 – 36 , 43 – 61 odd, 71, 73) 47) 2.007 49) -3.776 51) 9.285 53) -0.014 55) 25.714° 57) 337.5° 59) -756° 61) -114.592° 71) 6/5 rad 73) 32/7 rad

4.2 Trigonometric Functions: The Unit circle Objective: Evaluate trigonometric functions Use period to evaluate trigonometric functions Evaluate trigonometric functions with a calculator.

The Unit Circle with Radian Measures

Do you remember 30º, 60º, 90º special right triangles? long leg hypotenuse short leg Hypotenuse = double the short leg short leg = half the hypotenuse  

The Unit Circle with Radian Measures 1 2 , 3 2 1 30o   60o 1/2 Hypotenuse = double the short leg short leg = half the hypotenuse long leg = short leg times

The Unit Circle with Radian Measures − 1 2 , 3 2 1 2 , 3 2 − 3 2 , 1 2 3 2 , 1 2 30o 60o 1 𝟏 𝟐 𝟑 𝟐 − 3 2 , − 1 2 3 2 , − 1 2 − 1 2 ,− 3 2 1 2 ,− 3 2

Do you remember 45º, 45º, 90º isosceles right triangles?  

The Unit Circle with Radian Measures leg = hypotenuse times 45o 1   2 2 , 2 2

The Unit Circle: Radian Measures and Coordinates Trigonometric Functions: Let t be a real number and let (x, y) be the point on the unit circle corresponding to t sin t = y csc t = 1 𝑦 cos t = x sec t = 1 𝑥 tan t = 𝑦 𝑥 cot t = 𝑥 𝑦 (cos t, sin t)

Angles and the Unit Circle Find the exact values of cos (–150°) and sin (–150°). sin t = y csc t = 1 𝑦 cos t = x sec t = 1 𝑥 tan t = 𝑦 𝑥 cot t = 𝑥 𝑦 sin −150° =− 1 2 cos −150° =− 3 2

Find the six trig functions for 2𝜋 3 sin t = y csc t = 1 𝑦 cos t = x sec t = 1 𝑥 tan t = 𝑦 𝑥 cot t = 𝑥 𝑦 sin 2𝜋 3 = 3 2 cos 2𝜋 3 =− 1 2 tan 2𝜋 3 = csc 2𝜋 3 = sec 2𝜋 3 = cot 2𝜋 3 =

Example: Evaluate the six trigonometric functions of − 𝜋 4

Even and Odd Trig Functions: Even: cos(-t) = cost sec(-t) = sect Odd: sin(-t) = -sint tan(-t) = -tant csc(-t) = -csct cot(-t) = -cott

Using the Period to Evaluate Sine and Cosine:

Evaluating Trig Functions with a Calculator: 1) csc 𝜋 8 = 1 𝑠𝑖𝑛 𝜋 8 Mode: Radian 1  sin (   8 ENTER Display: 2.6131… 2) Sin 76.4 Mode: Degree Sin 7 6 . 4 ENTER Display: 0.0709…

Display: 0.0709… Evaluating Trig Functions with a Calculator: 2) cot 1.5 Mode: Radian 1  tan ( 1 . 5 ENTER Display: 0.0709…

Evaluate the six trigonometric functions of − 9𝜋 4 Sneedlegrit: Evaluate the six trigonometric functions of − 9𝜋 4 HW: Pg377- 8 (2 – 30 even, 33, 37, 39, 41, 45, 47, 51) Timed Five Minute Quiz on Unit Circle tomorrow!