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

Example:

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

INVERSE example: INVERSE Function Machine

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

sin( ) 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝜃 𝜃

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.

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin-1( ) 𝑜𝑝𝑝 ℎ𝑦𝑝 𝜃

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

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

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

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

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