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**an input/output machine where…**

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

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Example:

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**So what does an INVERSE function do?**

It reverses the process of a function. Consequently, it changes the outputs BACK to inputs.

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INVERSE example: INVERSE Function Machine

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**What about trigonometric functions?**

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

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sin( ) 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 𝜃 𝜃

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**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.

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𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 sin-1( ) 𝑜𝑝𝑝 ℎ𝑦𝑝 𝜃

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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

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

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

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

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

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9.5 Trigonometric Ratios Sin-Cos-Tan. What is Trigonometry? Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics.

9.5 Trigonometric Ratios Sin-Cos-Tan. What is Trigonometry? Trigonometry (from Greek trigōnon "triangle" + metron "measure") is a branch of mathematics.

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