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 FunctionMachine

What about trigonometric functions?

• Sine, cosine, and tangent have ANGLES as inputs.

• Their outputs are a ratio of sides (Remember Soh-Cah-Toa)

𝜃 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒sin( )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.

𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒h𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒

sin-1( ) 𝜃𝑜𝑝𝑝h𝑦𝑝

tan−1(𝑜𝑝𝑝𝑎𝑑𝑗 )=𝜃cos−1( 𝑎𝑑𝑗h𝑦𝑝 )=𝜃

sin−1(𝑜𝑝𝑝h𝑦𝑝 )=𝜃𝑠𝑖𝑛 (𝜃 )=𝑜𝑝𝑝h𝑦𝑝

𝑐 𝑜𝑠 (𝜃 )= 𝑎𝑑𝑗h𝑦𝑝

𝑡 𝑎𝑛 (𝜃 )=𝑜𝑝𝑝𝑎𝑑𝑗

FUNCTION INVERSE FUNCTION

Choose the OUTPUT…

𝜶

𝜷B

AC

sin (𝛼 )=¿ ¿BC AB

Choose the OUTPUT…

𝜶

𝜷B

AC

sin ( 𝛽)=¿¿

CA

AB

Choose the OUTPUT…

𝜶

𝜷B

AC

sin−1( 𝐴𝐶𝐴𝐵 )=¿¿ 𝜷

Choose the OUTPUT…

𝜶

𝜷B

AC

tan−1( 𝐴𝐶𝐶𝐵 )=¿¿ 𝜷