Hamilton's Math To Build On - copyright 1993

Using the Inverse Key

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* Using the Inverse Key

The fact that the calculator has keys for only half the functions and arc functions is not an oversight on the part of the manufacturers. It is pure economics. Why should they put six keys on a calculator when one key, the inverse key 1/x, will do the same work?

Look at the symbol on the inverse key. It is a fraction with a variable as the denominator. That variable will be whatever is in the display when you push the inverse key. If you have 2 on the display and push 1/x, the display will show 0.5, which is equal to 1/2. The inverse key replaces the variable x with the number in the display and gives you the answer in the format of a decimal point fraction.


* Using the Inverse Key with Functions

Let's turn to the functions and see how they work with this inverse key.

Notice that the numerator and denominator of the cosecant, H/O, are the reverse of the sine, O/H. They have an inverse relationship. In fact, all the functions on the right are inverse to the functions on the left, and vice versa.

For example: With the 3-4-5 right triangle, the Sin = 3/5 and the Csc = 5/3. 3/5 = 0.6 and 5/3 = 1.67

This chart shows these inverse relationships.

To determine a function using the inverse key:

  • First: Determine the function which is inverse to the function you want.
  • Second: Do your calculations based on that function.
  • Third: Push the inverse key 1/x.

For example, to find the cosecant of an angle:

  • First: Find the sine of the angle.
  • Second: Use the inverse key 1/x to find the cosecant of the angle.

    When you enter the sine of an angle into the calculator and push the inverse key, you have 1/sin, which is the cosecant of that angle.

For example: The cosecant of 24° is found in this manner.

The cosecant of 24° is 2.4589.

Using the Inverse Key with Functions: Practice

Find the indicated function for each angle below. Round off to 4 decimal places.

Remember: Use the calculator key that is the inverse of these functions first, then the 1/x key.

   (1)  csc 40°         (5)  cot 60° 
   (2)  sec 45°         (6)  csc 24° 
   (3)  cot 34°         (7)  sec 65° 
   (4)  sec 12°         (8)  cot 1° 

On to Using the Inverse Key with the Arc Functions

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16 September 1995
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