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LG 2-3 Inverse Trig Functions

LG 2-3 Inverse Trig Functions. What is an inverse trig function?. Instead of telling me the coordinate for the angle, you will tell me the angle given a coordinate. The inverse of a function can be found by reversing the order of each ordered pair in the given function.

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LG 2-3 Inverse Trig Functions

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  1. LG 2-3 Inverse Trig Functions

  2. What is an inverse trig function? • Instead of telling me the coordinate for the angle, you will tell me the angle given a coordinate.

  3. The inverse of a function can be found by reversing the order of each ordered pair in the given function.

  4. Inverse Cosine Function • The cosine function for (-∞,+ ∞) in NOT one-to-one because a horizontal line would intersect the graph more than once. • Therefore, the inverse relationship would NOT be a function because it wouldn’t pass the vertical line test. • The only way to make the inverse cosine function is by restricting the domain of the cosine function. • The domain restriction for cosine is [0,∏]

  5. Inverse Cosine Graph • The easiest way to graph the inverse cosine graph is to set up a t-table for cosine, and then invert the coordinates. • The domain (x) of the cosine function becomes the range (y) of the inverse cosine function and vice versa.

  6. Domain and Range of Inverse Cosine • Express the domain and range of the inverse cosine function • Since it is the inverse, they just change spots! • Make sure you are listing the restricted domain and range!

  7. Other Inverse Trig Functions ARCSINE • The sine graph also has to be restricted in order to have an inverse. Graph it now on your calculator. What do you think it should be restricted to? • [-90,+90] ARCTANGENT • The tangent should also be restricted. It may be a little easier to see. Graph it on your calculator. What should the domain restriction be? • [-90,+90]

  8. Inverse Reciprocal Functions • Continue making graphs of the rest of the inverse trig functions: • arcsecant(x) • arccosecant(x) • arccotangent(x)

  9. Ranges and Domains of Inverse Trig Functions

  10. Examples:

  11. Sometimes, you will encounter the composition of trig functions with inverse trig functions. The following are pretty straightforward compositions. Did you suspect the answer was going to be 120o? This problem behaved differently because 120o is outside the range of the arcsin. So use some caution when evaluating the composition of inverse trig functions.

  12. Practice Negative ratios for arccos generate angles in Quadrant _____ Negative ratios for arcsin generate angles in Quadrant _____ Negative ratios for arctan generate angles in Quadrant _____ Complete the problems on the back of your warm up

  13. How to check your answers… • Use the “second” feature on your calculator • 2nd SIN(-.5) = • *your calc should be in degree mode or you will get a rounded radian answer • For the secant, cosecant, or cotangent functions: • 2nd SIN ( 1/ #) = • For composition problems, you can enter them straight into your calc • 2nd SIN (SIN (270o) =

  14. Find the exact value of each expression without using a calculator. Express your answer in radians.

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