2-5: Inverse Trigonometric Functions and Triangle Problems

Hey guys... =]

Definitons:

If x is the value of a trigonometric function at angle θ, then the inverse trigonometric functions are:
The principal branch is the portion of the graph that is one-to-one (invertible). When finding the value of an angle from an inverse trigonometric function, your calculator gives you the value that rests on this branch of the graph. This is to ensure the graph of the inverses of the sin/cos/tan functions will also be functions.

For example:

The domain and range of sin x is the range and domain of its inverse.

Example triangle problem:
A ship is passing throught a strait and is 2400 m away from an island as determined by radar. Later, the radar determines that the ship is 2650 m away. By what angle (theta) did the ship's bearing change?

Explanation: Cosine is a ratio of adjacent over hypotenuse, in this case 2400/2650. The inverse cos function is looking for the angle whose ratio of adj/hyp is 2400/2650. We solve to get 25.1 degrees.

Be Careful!:

Additional Internet Resources:
Inverse trig functions
Useful symbols (such as theta)

Edward - Remember to post the next set of notes!

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