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

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°