What is a FUNCTION? an input/output machine where… • …each input has EXACTLY one output. • …outputs are 100% predictable.
Inverse Trig Functions
Jul 15, 2015
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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)
𝜃𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒sin( )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
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒sin-1( ) 𝜃
𝑜𝑝𝑝
ℎ𝑦𝑝
tan−1𝑜𝑝𝑝
𝑎𝑑𝑗= 𝜃
cos−1𝑎𝑑𝑗
ℎ𝑦𝑝= 𝜃
sin−1𝑜𝑝𝑝
ℎ𝑦𝑝= 𝜃𝑠𝑖𝑛 𝜃 =
𝑜𝑝𝑝
ℎ𝑦𝑝
𝑐𝑜𝑠 𝜃 =𝑎𝑑𝑗
ℎ𝑦𝑝
𝑡𝑎𝑛 𝜃 =𝑜𝑝𝑝
𝑎𝑑𝑗
FUNCTION INVERSE FUNCTION
Choose the OUTPUT…
𝜶
𝜷
B
AC
sin 𝛼 =
BC AB
Choose the OUTPUT…
𝜶
𝜷
B
AC
sin 𝛽 =
CA
AB
Choose the OUTPUT…
𝜶
𝜷
B
AC
sin−1𝐴𝐶
𝐴𝐵=
𝜷
Choose the OUTPUT…
𝜶
𝜷
B
AC
tan−1𝐴𝐶
𝐶𝐵=
𝜷
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