What is a FUNCTION? an input/output machine where… …each input has EXACTLY one output....
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Transcript of What is a FUNCTION? an input/output machine where… …each input has EXACTLY one output....
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