Calculate Sin/Cos/Tan By Hand - No Calculator Needed!

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In summary, there is a numerical method to calculate values for sin (42°), sin (43°), sin (44°) etc by hand. This method involves converting the values to radians and using the Taylor series for sin and cos near zero. By approximating sin and cos to their first few terms, accurate values can be obtained for the given examples.
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Goliatbagge
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Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?
 
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Goliatbagge said:
Does it exist a numerical method to calculate for example sin (42°), sin (43°), sin (44°) etc by hand?

Of course you will turn these into radians ... but since all of your values are near [itex]\pi/4[/itex], I would use,
[tex]
\sin ( \pi/4 + x) = \sin(\pi/4) \cos(x) + \sin(x) \cos(\pi/4) = \left(\cos(x) + \sin(x) \right) / \sqrt{2}.
[/tex]
Your values of [itex]x[/itex] are [itex]-\pi/180, -2 \pi/180, - 3 \pi/180, ...[/itex] which are small, so you can take the first few terms in the Taylor series for sin and cos near zero. Even approximating [itex]\cos(x) \approx 1[/itex] and [itex]\sin(x)\approx x[/itex] should get you several correct digits for the exact examples you gave.

jason

EDIT: I now see that this was included in adjacent's link above. I had just read the first part with the Taylor series about zero ... Oops!
 
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1. How do I calculate sin, cos, and tan without a calculator?

To calculate sin, cos, and tan without a calculator, you can use the basic trigonometric identities and formulas. For example, sin = opposite/hypotenuse, cos = adjacent/hypotenuse, and tan = opposite/adjacent. You can also use the unit circle or memorize common values for sin, cos, and tan.

2. Why is it important to be able to calculate sin, cos, and tan by hand?

Calculating sin, cos, and tan by hand is important because it helps you understand the underlying concepts and principles of trigonometry. It also allows you to verify the accuracy of your answers when using a calculator and can be useful in situations where a calculator is not available.

3. Can I use a calculator to check my answers when calculating sin, cos, and tan by hand?

Yes, you can use a calculator to check your answers when calculating sin, cos, and tan by hand. However, it is important to note that calculators may round off values, so your answers may not be exact.

4. What are some tips for calculating sin, cos, and tan by hand?

Some tips for calculating sin, cos, and tan by hand include understanding the relationship between the trigonometric functions and the unit circle, memorizing common values, using the appropriate trigonometric formulas, and practicing regularly to improve your skills.

5. Are there any shortcuts for calculating sin, cos, and tan by hand?

There are some shortcuts for calculating sin, cos, and tan by hand, such as using the Pythagorean identities and the sum and difference formulas. However, these shortcuts may not always be applicable and it is important to have a solid understanding of the concepts and principles behind the calculations.

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