The first quadrant is the top, right side of the circle. It’s the part of the circle where both the x-coordinate and the y-coordinate are positive. As you move into other quadrants, the angle measurement will change. However, the coordinates for sine and cosine will be the same integer, though they may shift from positive to negative. That means you can use your left hand trick to find the coordinates in any quadrant! Here’s how to label your fingers:  Use your pinky to represent a 0 degree angle. The 0 degree angle falls on your x-axis. It’s the starting point of your circle, which is why it’s 0. Your ring finger represents a 30 degree angle. Let your middle finger represent a 45 degree angle. Your index finger represents a 60 degree angle. Make your thumb represent the 90 degree angle. Put down the finger you’re using to represent the angle you want to find the cosine for. Count the number of fingers to the left of the finger that represents your angle. Then, take the square root of this number and divide it by 2 to find your coordinates.  For example, if you were finding the coordinates for a 30 degree angle, you’d put down your ring finger. To the left of that finger, you have your thumb, index finger, and middle finger, which means 3 fingers. This means the cosine coordinate is 32{\displaystyle {\frac {\sqrt {3}}{2}}}. This is your final answer since you can't simplify the fraction any further. If you were getting the cosine for a 0 degree angle, you’d put down your pinkie and count 4 fingers to the left. Your equation is 42{\displaystyle {\frac {\sqrt {4}}{2}}}. Since the square root of 4 is 2, you’d solve 2/2=1. This is your cosine. Put your finger down again, then count the number of fingers to the right. Take the square root of this number, then divide it by 2.  In the example above, you’d see that for a 30 degree angle you only have one finger to the right, your pinky finger. That means your sine coordinate would be 12{\displaystyle {\frac {\sqrt {1}}{2}}}. Since the square root of 1 is 1, you can just write 1/2. For your 0 degree angle, you’d see that there are no fingers to the right of your pinky. This means your sine must be 0. Each quadrant has its own different positive or negative charge. It’s easiest to see this charge when you look at the circle on a grid. The first quadrant is between the positive x-axis and positive y-axis, so both coordinates are positive. The second quadrant is between the positive y-axis and negative x-axis, so it will be negative, positive. Here’s how each coordinate is charged in each quadrant:  Quadrant 1 coordinates are (+,+). Quadrant 2 coordinates are (-,+). Quadrant 3 coordinates are (-,-). Quadrant 4 coordinates are (+,-). You can use the hand trick to fill in the coordinates for each quadrant, even though the angles are different. Just remember to switch up the positive or negative charges depending on the quadrant you’re doing.
افرد كفك الأيسر بحيث يشكل إصبعي الإبهام والخنصر زاوية قائمة. تخيل إن كل إصبع يمثل زاوية في الربع الأول. جد قيم دالة جتا لأي زاوية عن طريق عد الأصابع ناحية اليسار. جد دالة جا لأي زاوية بعد الأصابع إلى اليمين. غيّر إشارات الإحداثيات للحصول على قيم الدوال في الأرباع الأخرى. تعرّف على جميع إحداثيات دائرة الوحدة باستخدام حيلة اليد.