1 00:00:00,660 --> 00:00:04,800 High students, welcome to this section where we deal with trigonometry. 2 00:00:05,130 --> 00:00:09,610 Now let's get started understanding some of the basic terminology in trigonometry. 3 00:00:10,030 --> 00:00:13,890 Over here, I have a right angle triangle ABC. 4 00:00:14,130 --> 00:00:14,520 Right. 5 00:00:15,070 --> 00:00:17,880 You can see this angle over here is a 90 degree angle. 6 00:00:18,090 --> 00:00:20,580 Now, let's take that this angle. 7 00:00:20,580 --> 00:00:22,440 It is theta degrees. 8 00:00:22,950 --> 00:00:23,520 All right. 9 00:00:23,790 --> 00:00:26,850 Now, then I can see that side. 10 00:00:26,850 --> 00:00:31,640 EBR is the Eddison side for Angle Theta, right. 11 00:00:31,860 --> 00:00:34,470 It's the side that is at the center data. 12 00:00:34,620 --> 00:00:37,940 And you can't take the hypotenuse as the adjacent side. 13 00:00:37,950 --> 00:00:42,420 Right in this triangle is the hypotenuse and Abey's is one more side. 14 00:00:42,660 --> 00:00:45,150 So these two sides are next to detA. 15 00:00:45,360 --> 00:00:50,950 Now the adjacent side is the side that is next to Peter and is not the hypotenuse. 16 00:00:51,150 --> 00:00:51,550 All right. 17 00:00:51,810 --> 00:00:53,480 Now you can see that side. 18 00:00:53,490 --> 00:00:57,780 ABC is the opposite side or angle Teater. 19 00:00:58,110 --> 00:01:02,700 So Abe is the adjacent side and Beezy is called the opposite side. 20 00:01:02,910 --> 00:01:05,610 And remember, Acey is the hypotenuse. 21 00:01:05,760 --> 00:01:09,280 That is it's the side that is opposite the 90 degree angle. 22 00:01:09,660 --> 00:01:10,100 All right. 23 00:01:10,320 --> 00:01:15,040 Now, we have learned these two important terminologies that we use in trigonometry. 24 00:01:15,370 --> 00:01:20,010 Now let's get into S.T. de Costa and a.T.M. 25 00:01:20,280 --> 00:01:26,040 First, we will understand what we mean with this, and then we will learn some interesting things about 26 00:01:26,040 --> 00:01:26,370 this. 27 00:01:26,640 --> 00:01:27,060 All right. 28 00:01:27,240 --> 00:01:29,330 Let's get started over here again. 29 00:01:29,340 --> 00:01:33,880 I have my triangle, ABC and this angle over here is the study group. 30 00:01:34,170 --> 00:01:35,820 Now, let's take an example. 31 00:01:35,970 --> 00:01:40,050 Let the sides of this triangle be three, four and five centimeter. 32 00:01:40,290 --> 00:01:40,740 All right. 33 00:01:40,920 --> 00:01:42,990 Now, let's start with sine data. 34 00:01:43,740 --> 00:01:49,200 Sine Deda is defined as the opposite side, divided by the hypotenuse. 35 00:01:49,440 --> 00:01:51,940 Now, over here we have pizza right now. 36 00:01:51,960 --> 00:01:54,510 Let's find S.T. for this angle. 37 00:01:54,810 --> 00:01:58,310 So that would be the ratio between four, right? 38 00:01:58,470 --> 00:02:00,180 Because four is the opposite side. 39 00:02:00,300 --> 00:02:00,660 Right. 40 00:02:00,670 --> 00:02:04,020 This is the side opposite the double and the hypotenuse. 41 00:02:04,230 --> 00:02:05,940 The hypotenuse is easy. 42 00:02:05,970 --> 00:02:07,480 That's five units over here. 43 00:02:07,800 --> 00:02:11,530 So done in this case is four divided by five. 44 00:02:11,880 --> 00:02:16,350 Now, if this angle over here is Alpha, let's find sine Alpha. 45 00:02:16,350 --> 00:02:19,740 Also sign Alpha is opposite side by hypotenuse. 46 00:02:20,070 --> 00:02:23,970 The side opposite alpha is equal to three centimetre. 47 00:02:23,970 --> 00:02:24,290 Right. 48 00:02:24,420 --> 00:02:25,680 This is the opposite side. 49 00:02:25,680 --> 00:02:26,030 Right. 50 00:02:26,250 --> 00:02:27,150 So that's three. 51 00:02:28,190 --> 00:02:34,610 And you divide it by the hypotenuse, that's easy, which is equal to five centimeter, so sine alpha 52 00:02:34,610 --> 00:02:36,770 over here is equal to three by five. 53 00:02:37,220 --> 00:02:37,630 All right. 54 00:02:38,180 --> 00:02:42,840 We have seen that SINTA is equal to opposite side by hypotenuse. 55 00:02:43,130 --> 00:02:43,610 All right. 56 00:02:44,360 --> 00:02:48,290 Now let's proceed and find what we mean with cost theta. 57 00:02:48,620 --> 00:02:49,100 All right. 58 00:02:49,340 --> 00:02:55,010 Gosta is defined as the ratio between the adjacent side and the hypotenuse. 59 00:02:55,310 --> 00:02:57,920 So in this case, over here you have Titta. 60 00:02:58,160 --> 00:03:03,050 So which is the adjacent side to angle to that side Ebright. 61 00:03:03,230 --> 00:03:06,580 Therefore Kosti will be equal to three. 62 00:03:06,770 --> 00:03:12,950 That's the adjacent side divided by the hypotenuse which is Acey, and that's equal to five because 63 00:03:13,010 --> 00:03:14,210 it is equal to three by five. 64 00:03:14,420 --> 00:03:21,500 Now let's find course Alpha also to the adjacent side to Alpha is B.C. right is the side next to Alpha. 65 00:03:21,530 --> 00:03:22,760 Other than the hypotenuse. 66 00:03:23,030 --> 00:03:24,970 So we have B.C. over here, right? 67 00:03:25,130 --> 00:03:26,960 That's the adjacent side. 68 00:03:26,960 --> 00:03:29,720 And the hypotenuse is E, C, that's five. 69 00:03:29,720 --> 00:03:32,380 So cos Alpha is equal to four by five. 70 00:03:32,780 --> 00:03:33,240 All right. 71 00:03:33,440 --> 00:03:35,360 So we have seen sine data and. 72 00:03:36,410 --> 00:03:44,480 Now let's see the third important ratio that Santita and tanty is defined as the opposite side, divided 73 00:03:44,480 --> 00:03:45,770 by the adjacent side. 74 00:03:46,070 --> 00:03:47,810 Now over here you have titta. 75 00:03:47,960 --> 00:03:49,910 The opposite side is four, right. 76 00:03:50,150 --> 00:03:56,570 So in this ratio the numerator is equal to four and the adjacent side would be three. 77 00:03:56,570 --> 00:03:56,900 Right. 78 00:03:57,050 --> 00:03:58,440 So you have three over here. 79 00:03:58,670 --> 00:04:00,980 So Tante is equal to four by three. 80 00:04:01,250 --> 00:04:06,170 Now can you tell me what would be an Alpha and alpha would be three by four. 81 00:04:06,230 --> 00:04:06,530 Right. 82 00:04:06,800 --> 00:04:10,060 Because three is the opposite side and four is the adjacent. 83 00:04:10,580 --> 00:04:17,030 Now, an interesting thing to note over here is that data can also be obtained by taking the ratio of 84 00:04:17,030 --> 00:04:19,270 sine detA and Kerstetter. 85 00:04:19,520 --> 00:04:23,060 Now, what is Santita S.D. four divided by five. 86 00:04:23,060 --> 00:04:23,340 Right. 87 00:04:23,650 --> 00:04:26,870 So let's write that and Kosti days three by five. 88 00:04:26,870 --> 00:04:28,530 Right adjacent by opposite. 89 00:04:28,550 --> 00:04:29,280 So three by five. 90 00:04:29,520 --> 00:04:34,790 Now when you take the ratio of four by five, divided by three by five, this five and this five gets 91 00:04:34,790 --> 00:04:37,430 canceled and you are left with four by three. 92 00:04:37,550 --> 00:04:40,640 So tanty is also equal to sign. 93 00:04:40,640 --> 00:04:42,240 detA by Kosti to.