How to memorize Special Angles in Trigonometry ( Maths)

Hi students,

Today someone asked about how to memorize special angles and the value of trigo functions in the quadrants.

In trigonometry there are 5 angles which are worthed memorizing after you understand why they are that way in the fiirst place. The angles 0, 30, 45, 60 and 90 are called special angles in trigonometry.

The side lengths of a 30–60–90 triangle

The side lengths of a 45–45–90 triangle

 
How do we memorize these?

As mentioned earlier, these angles 0°, 30°, 45°, 60°, and 90° are referred to as special angles in trigonometry. If you know the values of the sine function for the five angles, then you can easily determine the exact values of the other trig function.

This little trick gives the exact values of the sine function:

sin(0°)=½√0
sin(30°)=½√1
sin(45°)=½√2
sin(60°)=½√3
sin(90°)=½√4
By arranging the value of angle for each sine, write down 1/2 and from top down write square root of  0, 1, 2, 3, 4 in sequence.

As an example sin(45°)=½√2 is also the same as writing sin(45°)=1/square root of 2 . Do not get confused with the square root sign, the final value is the same. Another example for sin(90°)=½√4 it is the same as writing sin(90°)=½(2)= 1!!

The above arrangement is a tip to memorize or getting the values of sine, cosine and tangents for the five angles without checking your calculator.




On the values ( whether negative or positive) here is another useful tip in memorizing the values of trigonometric functions for each quadrants. This is applicable for both form 3 students working on their trigonometry introductionary class ( cosine, sine and tangent) and even for the more advanced like those taking SPM ( includes cot, cosec and sec).

All-Star Trig Class.

To memorize the three "standard" trigonometric functions which are positive in a given quadrant. Another variant is to use "All Students Take Calculus" as well which indicates the first letter of the trigonometry functions with  positive values. All (sine, cosine and tangent) in quadrant one, only Sine in quadrant two, tangent in quadrant three and cosine in quadrant four.






p/s These are borrowed open secrets and have been used by my maths teachers and are seen everywhere on the net, I really do not know the origins.

Image of triangle and table credit: https://en.wikipedia.org/wiki/Special_right_triangles
All star trig class image: http://en.wikibooks.org/wiki/High_School_Trigonometry/Relating_Trigonometric_Functions