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# Math12 lesson7

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• ### Math12 lesson7

1. 1. INVERSE TRIGONOMETRIC FUNCTIONS <br />
2. 2. DEFINITION: If is a one-to-one function with domain A and range B, then its inverse is the function with domain B and range A defined by <br />For a function to have an inverse, it must be one-to-one. Since the trigonometric functions are not one-to-one, they do not have inverses. It is possible, however, to restrict the domains of the trigonometric functions in such a way that the resulting functions are one-to-one.<br />
3. 3. Inverse trigonometric functions are defined as follows:<br />y<br />x<br />o<br />y = sinx<br />y<br />x<br />y = sin-1 x<br />
4. 4. y<br />x<br />o<br />y = cosx<br />y<br />x<br />y = cos-1 x<br />
5. 5. y<br />x<br />o<br />y = tanx<br />y<br />x<br />y = tan-1 x<br />
6. 6. y<br />x<br />o<br />y = cotx<br />y<br />x<br />y = cot-1 x<br />
7. 7. y<br />x<br />o<br />y = secx<br />y<br />x<br />y = sec-1 x<br />
8. 8. y<br />x<br />o<br />y = cscx<br />y<br />x<br />y = csc-1 x<br />
9. 9. EXAMPLE:<br />Find the exact values of the following:<br />
10. 10.
11. 11.
12. 12. II. Solve for x:<br />
13. 13. EXERCISES:<br />Find the exact values of the following:<br />