Trigonometry
Radius is calculated through angle, arc length and area of the sector
Transcript
00:00This is question number 4 exercise 6.2 we have to find the radius of the circle
00:06for the following information, you have to find the radius of the circle, you have
00:12information given is length rk, length r is 4 centimeters, theta is your angle
00:18is pi radians, first of all you have to tell the formula for this, we have
00:23to find the radius of the circle, first of all you have to find the radius of the circle,
00:53first of all you have to find the radius of the circle, first of all you have to find
01:00the radius of the circle, first of all you have to find the radius of the circle,
01:05first of all you have to find the radius of the circle,
01:08first of all you have to find the radius of the circle,
01:11first of all you have to find the radius of the circle,
01:14first of all you have to find the radius of the circle,
01:17first of all you have to find the radius of the circle,
01:20first of all you have to find the radius of the circle,
01:23first of all you have to find the radius of the circle,
01:26first of all you have to find the radius of the circle,
01:29first of all you have to find the radius of the circle,
01:32first of all you have to find the radius of the circle,
01:35first of all you have to find the radius of the circle,
01:38first of all you have to find the radius of the circle,
01:41first of all you have to find the radius of the circle,
01:44first of all you have to find the radius of the circle,
01:47first of all you have to find the radius of the circle,
01:50first of all you have to find the radius of the circle,
01:53first of all you have to find the radius of the circle,
01:56first of all you have to find the radius of the circle,
01:59first of all you have to find the radius of the circle,
02:02first of all you have to find the radius of the circle,
02:05first of all you have to find the radius of the circle,
02:08first of all you have to find the radius of the circle,
02:11now again if angle is 15 degrees,
02:15now it will change to aging,
02:18now again if angle is 15 degrees,
02:21now it will change to aging,
02:25if 1 degree is equal to 180 in radians,
02:28if 1 degree is equal to 180 in radians,
02:31will multiply to 1500 by 150 byрав는데
02:34will multiply to 1500 by1400 by180
02:36will multiply to 1400 by1400 by1400
02:39That's why we will put its value, when we will substitute its value, you will get 3.14
02:47over 180.
02:48If you calculate it with a calculator, you will get an angle of 0.2617 radians.
02:59Our angle was 15 degrees, but in formula whenever we use angle, our angle should be in radians.
03:06That's why we have converted this angle into radians.
03:10Now simply we will put it in the formula, value of L is 6, r is unknown to us, theta
03:20is 0.2617 radians, whatever you want to know, you can separate it, 6 divided by 0.2617,
03:33so r is going to be 22.92 meters, this is the radius.
03:42In the third part, we have area given and we have angle given, we have to find the radius.
03:48So first of all, you see that the angle you have is pi by 4 radians, we don't have to
03:54write pi, instead of pi you will write 3.14 divided by 4, your angle will be 0.785 radians.
04:07Now we will come to the formula of area of a circle, so the formula of area you have
04:13is half r square, sorry this is the formula for the sector, because the relation of arc
04:22with radius is with the sector.
04:26Now you see that the area you have is 200, we don't know the radius, theta we have,
04:35angle we have, that is 0.785.
04:40Now we will solve this, as you solve, calculate everything here and then isolate r square,
04:48so it is going to be 400 r square and 0.785,
04:59you have to isolate that, r square is equal to 400 and the multiplying,
05:10r square is 509.5,
05:19so
05:34and this is the final answer.
05:36Now come towards the fourth part of this question, this is the last part,
05:48so this is the formula of area of a sector, r square into theta,
06:08furthermore,
06:18now you see what is the formula of arc length, the formula of arc length is r theta.
06:25So instead of r and theta, I can simply write here 1 over 2 into r into l,
06:35I can do substitution easily, area is here 100 centimeter square, 1 by 2,
06:43r we have to find, arc length is 10 decimeters,
06:56I am taking 2 on the other side of equation,
07:05r is equal to 200,
07:12I take a 20 decimeter, this is the answer.