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7.1

7.1 . Inverse Trig Functions Sin,cos,tan. 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. Inverse Cos or arccos or cos -1 Dom: [-1,1] Range: [0 , π ]

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7.1

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  1. 7.1 Inverse Trig Functions Sin,cos,tan

  2. 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.

  3. Inverse Cos or arccos or cos-1 Dom: [-1,1] Range: [0, π] It looks like cos going up the y axis 0

  4. We pick the sin graph from –π/2 to π/2. We then reflect the indicated portion of y = sin x through the line y = x, we obtain the graph of y = arcsin x.

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

  6. 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 reals The range for arctan x is (-π/2 , π/2)

  7. arctan is the same as tan inverse or tan-1. y = tan-1x = arctan(x) In all of the inverse functions, 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

  8. Hw pg 451 13-24, 37-52 all Lets do some.

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