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

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

3. Learning Objective
To find inverse trig functions

4. 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

5. 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 −
= − 𝜋 3
= 𝑐𝑜𝑠 −1 −
4. 𝑐𝑜𝑠 −1 cos 7𝜋 6
= 5𝜋 6

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

7. 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

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

9. 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 −
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

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

11. 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

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

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

14. Ticket Out the Door
Find

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