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1.7

1.7 . Inverse Trig Functions Sin,cos,tan. The goal is to find, define and graph the inverse trig functions. An inverse function undoes another function. For example y = x 2 and y = √x Are inverses because they “undo” each other.

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1.7

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  1. 1.7 Inverse Trig Functions Sin,cos,tan

  2. The goal is to find, define and graph the inverse trig functions. An inverse function undoes another function. For example y = x2 and y = √x Are inverses because they “undo” each other. For our trig inverse functions were are going to put in values and get out angles.

  3. We choose the portion of y= cos(x) from x = 0 to x = π. We now reflect every point on this portion of the cos x curve through the line y = x.

  4. Inverse Cos or arccos Dom: [-1,1] Range: [0, π]

  5. we reflect the indicated portion of y = sin x through the line y = x, we obtain the graph of y = arcsin x:

  6. Inverse Sin or arcsin We are now putting In values and Getting out Angles. We always Restrict the inverse Graphs. Dom [-1,1] Range [-π/2, π/2]

  7. Reflecting this portion of the graph in the line y = x, we obtain the graph of y = arctan x The domain of arctan x is All values of x The range for arctan x is -π/2 ≤ arctan x ≤ π/2

  8. arctan is the same as tan inverse or tan-1. y = tan-1x = arctan We put in values and get out angles. Ex. sin-1(√2/2) = arcsin (√2/2) = what angle has a sin value of √2/2 and is between -π/2, π/2 = π/4 Functions and their inverses undo each other arcsin(sin(x)) = x

  9. HW pg 197 1-15 odd Draw arccos, arcsin, and arctan

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