1. Warm-up
Put the problems from the homework up on the board that you wish to review
Textbook pages #5-23 ODD, 59 and 61

2. Learning Goals
The student will be able to understand and apply the graphs of the six trigonometric functions and apply them to real-life scenarios.

3. Class Agenda Review Homework Evaluating Inverse Trig Functions Break
Properties of Inverse Trig Functions
Composition of Functions
Closure

4. Inverse Trig Functions
Option 1
Option 2
Read
sin −1 𝑥 =𝜃
arcsin 𝑥 =𝜃
The angle whose sin is:
cos −1 𝑥 =𝜃
arccos 𝑥 =𝜃
The angle whose cos is:
tan −1 𝑥 =𝜃
arctan 𝑥 =𝜃
The angle whose tan is:
csc −1 𝑥 =𝜃
arccsc 𝑥 =𝜃
The angle whose csc is:
sec −1 𝑥 =𝜃
arcsec 𝑥 =𝜃
The angle whose sec is:
cot −1 𝑥 =𝜃
arccot 𝑥=𝜃
The angle whose cot is:

5. Evaluating Inverse Trig Functions
arcsin −1 =
sin − =
arcsin =
arccos =
cos −1 − =
arctan 1 =
tan − =

6. Break

7. Properties of Inverse Trig Functions
Inverse Properties
𝐼𝑓 −1≤𝑥≤1 𝑎𝑛𝑑 − 𝜋 2 ≤𝜃≤ 𝜋 2 , 𝑡ℎ𝑒𝑛
sin arcsin 𝑥 =𝑥
arcsin sin 𝜃 =𝜃
𝐼𝑓 −1≤𝑥≤1 𝑎𝑛𝑑 0≤𝜃≤𝜋, 𝑡ℎ𝑒𝑛
cos arccos 𝑥 =𝑥
arccos cos 𝜃 =𝜃
𝐼𝑓 𝑥 𝑖𝑠 𝑎 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑎𝑛𝑑 − 𝜋 2 ≤𝜃≤ 𝜋 2 , 𝑡ℎ𝑒𝑛
tan arctan 𝑥 =𝑥
arcta𝑛 tan 𝜃 =𝜃

8. Composition of Functions
tan⁡( arctan −14) =
sin⁡( arcsin 𝜋) =
𝑐𝑜𝑠( arccos 0.54) =

9. Composition of Functions
tan arccos =
cos arcsin − =
𝑐𝑜𝑠 arctan − =
sin arccos =

10. Extra Practice
Textbook page 328 #29-61 ODD

11. Closure

12. Closure
How are the domain and range of the inverse trigonometric functions restricted?