1. an input/output machine where…
What is a FUNCTION?
an input/output machine where…
…each input has EXACTLY one output.
…outputs are 100% predictable.

2. Example:

3. So what does an INVERSE function do?
It reverses the process of a function.
Consequently, it changes the outputs BACK to inputs.

4. INVERSE example:
INVERSE
Function
Machine

5. What about trigonometric functions?
Sine, cosine, and tangent have ANGLES as inputs.
Their outputs are a ratio of sides (Remember Soh-Cah-Toa)

6. sin( )
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝜃 𝜃

7. How do INVERSE trigonometric functions work?
The input of an INVERSE trig function is a ratio of sides.
The output of an INVERSE trig function is an ANGLE.

8. 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
sin-1( )
𝑜𝑝𝑝 ℎ𝑦𝑝 𝜃

9. FUNCTION
INVERSE FUNCTION
sin −1 𝑜𝑝𝑝 ℎ𝑦𝑝 =𝜃
𝑠𝑖𝑛 𝜃 = 𝑜𝑝𝑝 ℎ𝑦𝑝
cos −1 𝑎𝑑𝑗 ℎ𝑦𝑝 =𝜃
𝑐𝑜𝑠 𝜃 = 𝑎𝑑𝑗 ℎ𝑦𝑝
𝑡𝑎𝑛 𝜃 = 𝑜𝑝𝑝 𝑎𝑑𝑗
tan −1 𝑜𝑝𝑝 𝑎𝑑𝑗 =𝜃

10. Choose the OUTPUT… 𝜶 𝜷 B A C
sin 𝛼 = AB BC

11. Choose the OUTPUT… 𝜶 𝜷 B A C
sin 𝛽 = AB CA

12. Choose the OUTPUT… 𝜶 𝜷 B A C
sin −1 𝐴𝐶 𝐴𝐵 = 𝜷

13. Choose the OUTPUT… 𝜶 𝜷 B A C
tan −1 𝐴𝐶 𝐶𝐵 = 𝜷