Trigonometry
Central angle is measured
Transcript
00:00Exercise 6.2, question number 3, find gradient measure of the central angle of circular sector
00:07of the following data, L you have is arc length, basically what is arc length, if you take
00:17any part of the circumference of the circle, then it is called arc length, we have radius
00:25is 8, radius is 4, and theta is unknown to us, so what we have to do, we have to find
00:32the angle, because of this arc length, what is the angle, first of all you should know
00:37the formula, very simple, L is equal to R theta, L is your arc length, R is your radius,
00:41and theta is your angle, now we have two values provided, and third we have to find, so what
00:48will you do, if you place the values, L is 8, radius is 4, and theta is unknown to us,
00:55theta is equal to 8, and the 4 which is multiplying will go to the other side and will get divided,
01:08so we will get the answer, 2 radians, whenever we calculate the angle from the formula, it
01:15will never be in degrees, it will always be in radians, come towards the second part of
01:20the same question, arc length you have is 8.5 meters, radius you have is 2.25 meters,
01:27and we have to find the angle, 8.5 meters is your arc length, radius you have is 2.5
01:36meters, and we have to know theta, because of this arc length, what will be the angle,
01:43first of all, radius and angle are directly proportional, L is equal to R theta is the
01:49formula, 8.5, radius we have is 2.25, theta we do not know, so what we will do, the thing
02:03which we have to know, we will isolate it, theta is equal to 8.5, which is multiplying
02:11by 2 radians, and we will get the answer, 3.78 radians, in third part, you have given
02:33area, radius, and we have to know the angle, this is also a simple question, first of all
02:40what you will do, you will mention the values given, from here it becomes clear that how
02:48we have to solve the question, area formula you have is 1 by 2, R square, theta, now you
02:58will see that the value of area is calculated here, so you will do substitution, you will
03:05write 45 instead of area, this is 1 by 2 here, radius you have is 10.70 square, and theta
03:17we do not know, so now what we will do, we will simply solve this, when you will solve
03:26this, you can directly solve this also,