1. Warm Up 30°±𝟑𝟔𝟎𝒏°, 150°±𝟑𝟔𝟎𝒏°, Solve in degrees: sin 𝜃= 1 2
Solve in radians: cos 𝜃=−
If 𝑠𝑖𝑛𝜃=− find 𝑐𝑜𝑡𝜃 in exact form.
If cos𝜃=− find 𝑐𝑠𝑐𝜃 in exact form.
What is the 𝑐𝑜𝑡𝜃÷𝑐𝑠𝑐𝜃÷𝑠𝑒𝑐𝜃?
𝟑𝝅 𝟒 ± 𝟐𝒏𝝅, 𝟓𝝅 𝟒 ±𝟐𝒏𝝅
− 𝟕𝟐 𝟕 =− 𝟔 𝟐 𝟕
Quad IV
𝟐 𝟑 𝟑
Quad II
𝒄𝒐𝒔 𝟐 𝜽

2. Section 7-6 The Inverse Trigonometric Functions
Objective: To find values of the inverse trigonometric functions

3. Trig FUNCTIONS Sine, cosine and tangent are all functions
Are they all one-to-one functions?

4. Does the graph have an inverse?
Domain:
Does the graph have an inverse?
No!
Notice how the axes are scaled!

5. How can you restrict the domain to make the graph one-to-one?

6. Tan x has an inverse. Domain: 𝑓 𝑥 =𝑇𝑎𝑛𝑥 Notice T is capitalized
Notice how the axes are scaled!

7. Notice how the axes are scaled!

8. How can you restrict the domain to make the graph one-to-one?
Notice how the axes are scaled!
How can you restrict the domain to make the graph one-to-one?

9. 𝑥 − 𝜋 2 ≤𝑥≤ 𝜋 2
Restrict domain to:

10. Inverse function is Sin-1 x
Notice how the axes are scaled!

12. 𝑓 𝑥 =𝑐𝑜𝑠𝑥
How can you restrict the domain to make the graph one-to-one?

13. Restrict domain to 0 <x < 

14. Notice the axes!
𝑭 −𝟏 𝒙 = 𝑪𝒐𝒔 −𝟏 𝒙

15. Q1 & Q4 - +
𝐶𝑜𝑠𝑥
𝑇𝑎𝑛𝑥
Q1 & Q2 -
Q1 & Q4 - + +
𝑆𝑖𝑛𝑥

16. Evaluate in radians without a calculator.
𝐶𝑜𝑠 −1 −
𝑆𝑖𝑛 −1 −1
𝑇𝑎𝑛 −1 (−1)
cos𝑥=− and 𝑄2
*If the angle is in Q4, write it as a negative angle.
𝐶𝑜𝑠 −1 − = 5𝜋 6
sin𝑥=−1 and 𝑄4
𝑆𝑖𝑛 −1 −1 =− 𝜋 2
tan𝑥=−1 and 𝑄4
𝑇𝑎𝑛 −1 −1 =− 𝜋 4

17. Inverse Trig Functions
Remember, finding the inverse is finding an angle!
𝑆𝑖𝑛 − =
30°
Because: Sin 30 °= 1 2

18. Example 1 Find Tan-1 2 in radians with a calculator.
First make sure your calculator is in the correct mode.

19. *If the angle is in Q4, write it as a negative angle.
Example 2
Find Tan-1 (-1) without a calculator.
angle
Domain of Tanx is − 𝜋 2 <𝑥< 𝜋 Q4
*If the angle is in Q4, write it as a negative angle.

20. Try without a calculator on #5 & 7 Unit circle is ok for both
Homework
Page 289 #1-15odd, 19, 21
Try without a calculator on #5 & 7
No calculator on #6 – 10
Unit circle is ok for both