Trigonometric Functions - 15, 75 Degrees

Category: Trigonometry

"Published in Suisun City, California, USA"

Without using a calculator, find the six trigonometric functions of 15º and 75º.

Solution:

Is it possible to find the six trigonometric functions for 15º and 75º without using a calculator? Well, we know the six trigonometric functions for the special angles such as 0º, 30º, 45º, 60º, and 90º. I am strongly advice that you must remember the trigonometric functions of special angles because you will use those later for proving of trigonometric identities, problem solving, and taking higher math subjects as well. Let's recall the six trigonometric functions of the special angles as follows

For 0º

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For 30º

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For 45º

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For 60º

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For 90º

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Therefore, using the Sum and Difference of Two Angles Formula, we have

Approximate Value - Square Root

Category: Differential Calculus, Arithmetic

"Published in Newark, California, USA"

Without using a calculator, find the approximate value of √101. 

Solution:

We know that the square root of 100 is 10. How do you get a square root of a number which is faster and easier than the traditional method without using a calculator? 

Well, let's consider this method using the principles of differentiation method. 

Let

then

If   x = 100
   dx = 101 - 100 = 1

then dy will be

Therefore

If you will use a calculator,√101 will be equal to 10.0498756211208902... which is close to the final answer.