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Wednesday, January 16, 2013

Approximate Value - Sine, Cosine, Tangent

Category: Differential Calculus, Trigonometry

"Published in Newark, California, USA"

Find the approximate values of trigonometric functions for 31° without using a calculator or trigonometric tables.

Solution:

Is it possible to get the six trigonometric functions of 31° without using a calculator or trigonometric tables? Yes, we can. We can get the approximate values of trigonometric functions of 31° by approximation and error method. 

We know that 30° is a special angle. The trigonometric functions for 30° are the following

         Sin 30° = 1/2                         Csc 30° = 2

         Cos 30° = 3/2                      Sec 30° = 2/3

         Tan 30° = 1/3                      Cot 30° = √3

Let 
                                               

If    



Therefore









using a calculator



from trigonometric table



Let



Therefore








using a calculator



from trigonometric table



Let



Therefore








or

using a calculator 



from trigonometric table



Let



Therefore








or

using a calculator



from trigonometric table



Let



Therefore








or

using a calculator



from trigonometric table



Let



Therefore








or

using a calculator



from trigonometric table



Note: All angles are converted from degrees into radians because radians are unitless and all trigonometric values are unitless.