# Finding Trig Ratios of Any Angle: A General & Easy Way

• The legend
In summary, there are a few ways to find the trigonometric ratios of any angle without using tables or a calculator. These include using a unit circle, Taylor expansion approximation, and double angle identities. However, some methods may be more time-consuming or less accurate than others. It is also possible to find resources and information on these methods through online sources such as Wikipedia.
The legend
Is there any general and hopefully 'easy' way to find the trigonometric ratios of any angle? That is without using the sin, cos etc tables?

If not any angle ... atleast whole number angles?

Do you mean also without a calculator?

If so, then the 'easiest' way that i can think of is to draw a unit circle on an x-y plane, use a protractor to draw a radius at the specific angle from the +x axis and then measure the x (cosine) and y (sine) coordinates of the point. Won't be the most accurate answer though, but it should be roughly around the correct value.

You could also use a Taylor expansion approximation and just take the first few terms?

Or else just use a calculator? Cant be easier than this :P

You can use the double angle identities and usually derive any angle just using the typical angles memorized using the unit circle.

yes, i did mean without a calc...
by the way what's this Taylor expansion approximation and how can i use it?
I did try googling but well didn't understand it.

The circle method is good though...

Feldoh said:
You can use the double angle identities and usually derive any angle just using the typical angles memorized using the unit circle.

hey i forgot that!
But nice idea!

The double and triple angle identities would be angels!

The legend said:
A series for a good approximation of all trig values(time consuming though)

http://en.wikipedia.org/wiki/Trigonometric_function#Series_definitions

(found 'em by googling and seeing wikipedia...never knew they were such good info givers)

If you going to try Taylor expansion's you don't want to use those expansions. Those series converge very slowly to the correct values. You could probably find a faster approximation somewhere.

## What is the purpose of finding trig ratios of any angle?

The purpose of finding trig ratios of any angle is to determine the relationship between the sides and angles of a right triangle. This is useful in various fields such as mathematics, engineering, and physics.

## What is the general and easy way to find trig ratios of any angle?

The general and easy way to find trig ratios of any angle is by using the mnemonic SOH-CAH-TOA. This stands for sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent. By remembering this, you can easily find the trig ratios of any angle.

## Do I need to know the exact angle measure to find trig ratios?

No, you do not need to know the exact angle measure to find trig ratios. As long as you know the side lengths of the triangle, you can use the inverse trigonometric functions on a calculator to find the angle measure and then use the SOH-CAH-TOA method to find the trig ratios.

## Are there any other methods to find trig ratios of any angle?

Yes, there are other methods to find trig ratios of any angle such as using trigonometric identities and the unit circle. However, the SOH-CAH-TOA method is the most commonly used and easiest method to find trig ratios.

## Why is it important to find the trig ratios of any angle?

It is important to find the trig ratios of any angle because it allows us to solve various real-world problems involving right triangles. This can help in fields such as navigation, construction, and surveying. Additionally, understanding trig ratios is fundamental in furthering our understanding of advanced trigonometric concepts.

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