Homework Log Mon 5/9 Lesson 8 – 7 Learning Objective: To inverse trig functions Hw: #818 Pg. 534 #15 – 28 all, 37 – 45 odd

5/9/16 Lesson 8 – 7 Inverse Trig Functions Day 2 Advanced Math/Trig

Learning Objective To find inverse trig functions

Inverse Trig Functions 𝑠𝑖𝑛 −1 sin 𝑥 =𝑥 Or arcsin sin x =x if − 𝜋 2 ≤𝑦≤ 𝜋 2 sin ( 𝑠𝑖𝑛 −1 𝑥)=𝑥 Or sin ( arcsin 𝑥 ) =𝑥 if −1≤𝑦≤1

Inverse Trig Functions 1. csc ( arccsc 3 ) ) =3 2. cos 𝑡𝑎𝑛 −1 3 = cos 𝜋 3 = 1 2 3. 𝑠𝑖𝑛 −1 sin 4𝜋 3 = 𝑠𝑖𝑛 −1 − 3 2 = − 𝜋 3 = 𝑐𝑜𝑠 −1 − 3 2 4. 𝑐𝑜𝑠 −1 cos 7𝜋 6 = 5𝜋 6

Inverse Trig Functions 5. sin 𝑐𝑜𝑠 −1 − 3 5 rainbow Let y= 𝑐𝑜𝑠 −1 − 3 5 5 4 y 𝜋 -3 since (–), in QII 4 5 sin 𝑦 = cos = CAH sin = SOH

Inverse Trig Functions 6. tan 𝑠𝑖𝑛 −1 − 12 13 𝜋 2 Let y= 𝑠𝑖𝑛 −1 − 12 13 5 banana − 12 5 y tan 𝑦 = –12 since (–), in QIV 13 − 𝜋 2 sin = SOH tan = TOA

Inverse Trig Functions 7. sin 𝑡𝑎𝑛 −1 6 8 𝜋 2 Let y= 𝑡𝑎𝑛 −1 6 8 10 6 y banana 6 10 = 3 5 sin 𝑦 = 8 since (+), in QI − 𝜋 2 tan = TOA sin = SOH

Evaluate Looks like sin (x + y) = sin 𝑥 cos 𝑦 + cos 𝑥 sin 𝑦 = 4 5 = 4 5 − 12 13 + 3 5 5 13 =− 33 65 Let 𝑥= 𝑡𝑎𝑛 −1 4 3 Let 𝑦= 𝑐𝑜𝑠 −1 − 12 13 𝑎𝑑𝑗 ℎ𝑦𝑝 𝑜𝑝𝑝 𝑎𝑑𝑗 𝜋 2 banana rainbow 5 cos 𝑥 = 3 5 cos 𝑦 =− 12 13 4 13 x 5 y 3 𝜋 -12 sin 𝑥 = 4 5 sin 𝑦 = 5 13 − 𝜋 2

Evaluate Looks like cos (2y) = 𝑐𝑜𝑠 2 𝑦− 𝑠𝑖𝑛 2 𝑦 = 11 6 2 − 5 6 2 = 11 6 2 − 5 6 2 =− 14 36 =− 7 18 Let 𝑦= 𝑠𝑖𝑛 −1 5 6 𝑜𝑝𝑝 ℎ𝑦𝑝 𝜋 2 banana 6 5 cos 𝑦 = 11 6 y 11 sin 𝑦 = 5 6 − 𝜋 2

Evaluate 10. sin 2 arccot − 4 3 Looks like sin (2y) =2 sin 𝑦 cos 𝑦 =2 3 5 − 4 5 =− 24 25 rainbow Let 𝑦= arccot − 4 3 𝑎𝑑𝑗 𝑜𝑝𝑝 5 3 y cos 𝑦 =− 4 5 𝜋 – 4 sin 𝑦 = 3 5

Evaluate 11. sin 2 arc𝑠𝑒𝑐 − 13 12 Looks like sin (2y) =2 sin 𝑦 cos 𝑦 =2 5 13 − 12 13 =− 120 169 rainbow Let 𝑦= arc𝑠𝑒𝑐 − 13 12 ℎ𝑦𝑝 𝑎𝑑𝑗 13 5 y cos 𝑦 =− 12 13 𝜋 – 12 sin 𝑦 = 5 13

Evaluate Looks like cos (x + y) = cos 𝑥 cos 𝑦 − sin 𝑥 sin 𝑦 = 4 5 = 4 5 − 5 13 − − 3 5 12 13 = 16 65 Let 𝑥= 𝑠𝑖𝑛 −1 − 3 5 𝑜𝑝𝑝 ℎ𝑦𝑝 Let 𝑦= 𝑐𝑜𝑠 −1 − 5 13 𝑎𝑑𝑗 ℎ𝑦𝑝 𝜋 2 banana rainbow cos 𝑥 = 4 5 cos 𝑦 =− 5 13 13 4 12 y x 𝜋 –3 sin 𝑥 =− 3 5 – 5 sin 𝑦 = 12 13 5 − 𝜋 2

Ticket Out the Door Find

Homework #818 Pg. 534 #15 – 28 all, 37 – 45 odd