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Secondary Circular Functions Help (page 2)

By — McGraw-Hill Professional
Updated on Oct 3, 2011

Values Of Circular Functions

Now that you know how the circular functions are defined, you might wonder how the values are calculated. The answer: with an electronic calculator! Most personal computers have a calculator program built into the operating system. You might have to dig around in the operating system folders to find it, but once you do, you can put a shortcut to it on your computer’s desktop. Use the calculator in the “scientific” mode.

The values of the sine and cosine function never get smaller than –1 or larger than 1. The values of other functions can vary wildly. Put a few numbers into your calculator and see what happens when you apply the circular functions to them. Pay attention to whether you’re using degrees or radians. When the value of a function “blows up” (the denominator in the unit-circle equation defining it becomes zero), you’ll get an error message on the calculator.

Secondary Circular Functions Practice Problems

Practice 1

Use a portable scientific calculator, or the calculator program in a personal computer, to find all six circular functions of 66°. Round your answers off to three decimal places. If your calculator does not have keys for the cosecant (csc), secant (sec), or cotangent (cot) functions, first find the sine (sin), cosine (cos), and tangent (tan) respectively, then find the reciprocal, and finally round off your answer to three decimal places.

Solution 1

You should get the following results. Be sure your calculator is set to work with degrees, not radians.

sin 66° = 0.914

cos 66° = 0.407

tan 66° = 2.246

csc 66° = 1/(sin 66°) = 1.095

sec 66° = 1/(cos 66°) = 2.459

cot 66 = 1/(tan 66°) = 0.445

Practice Problems for these concepts can be found at:  The Circle Model Practice Test

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