INTRODUCTION:
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We often think that math-related subjects are the difficult ones and can sometimes give us headache because of such terrible questions and problems that require us to think, solve, and analyze to find an answer. In that case, it would be much easier if we understand well all the concepts in math since every detail and lesson is really important in order to move on to the next level which also needs a higher thinking skills. So, mathematicians and other professionals or even a simple student like me is fund of basic tricks and techniques to easily get the right answer and at the same time to have fun while doing it.
OBJECTIVES:
• To be familiar with the Unit Circle
• To understand and memorize the Unit Circle coordinates in a second quadrant.
MATERIALS AND METHODS USED:
In this activity, we’re only be needing our left hand to perform this trick of getting the coordinates of the first quadrant in a unit circle and the rest is up to the brain to think. Although trigonometry is one of the hated branch of Mathematics because of its complicated and complex formulation of numbers, this is as simple as performing the four basic operations of elementary arithmetic. This discovery was introduced to us by our teacher in Grade 11 under our Pre-calculus subject. We were having a hard time in trigonometry, especially me because I don’t really know the unit circle and it is very difficult to familiarize the values of it.
Since the unit circle is defined as a circle with a radius of 1 and is centered at the origin (0,0), the angle drawn in the circle give the values of the trigonometric functions. These values involve different kinds of rational numbers which may result to confusion and may lead to the wrong answer. But, our teacher taught us a simple and helpful way on how to easily identify and memorize the coordinates of the unit circle by using our left hand. It is also known as the Left Hand Trick of Trigonometry. This technique helped me a lot in such a way that it leads me to arrive at the correct answer and it can also lessen my time in answering a problem.
Content:
The first thing you should know is that the left hand itself serves as the first quadrant of the unit circle which has a (+,+) coordinates. Since there are only five fingers, we can assign each finger to the most common radian or degree angle in the first quadrant. It is the 0°, 30°, 45°, 60° & 90°. Of course the assigned degree angle to the finger should follow the respective order and it is fixed to its position.
Pinky finger – 0°
Ring finger – 30°
Middle finger – 45°
Index Finger – 60°
Thumb – 90°
Notice that when you put a line on the thumb and on the pinky finger and extend it, it will create a perpendicular line which suggests a 90-degrees-angle and that’s what the first quadrant look like. Now, consider also your palm because you’ll need to put the answer on it. Just remember that your answer will be in fraction and will always have a denominator of two (2). So, we can easily arrive to the answer if we put a radical sign on the numerator (√/2) which is the formula and perform the main idea of this trick. After assigning and knowing all the needed values, let’s try out an example of determining the coordinates of any of the given measure in the unit circle.
First step:
Find a trigonometry problem, for example,
What is the sine and cosine of 30°?
Second step:
Hold down the finger assigned to the 30° angle, which is the
Ring finger
Third step:
Count the remaining finger on top of the assigned finger and put the answer under the radical sign of the given formula. The result will be the x-coordinate or the value of the cosine.
There are 3 fingers left on top of the assigned finger so, 3 should be placed under the radical sign of the given formula; √3/ 2 and that is the x-coordinate or cosine value of 30°.
Fourth step:
Count the remaining finger at the bottom of the assigned finger and put the answer under the radical sign of the given formula. The result will be the y-coordinate or the value of the sine.
There is only 1 finger left at the bottom of the assigned finger so, 1 should be placed under the radical sign of the given formula;√1/2 simplify if needed so the final answer will be ½ and that is the x-coordinate or cosine value of 30°.
Lastly, you can also find the value of the angles of the other quadrants since it just varies depending on the sign. There will be a little manipulation on the answer but once you knew and understood it well it will be easy for you.
Reference:
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