Trigonometry Basic P 1

追加: 2026-05-28

[00:00:12]Hi, let's talk about trigonometry.

[00:00:18]So what is trigonometry?

[00:00:20]So trigonometry is a branch of mathematics where we understand the relationship between the sides and the angle of any right angle triangle.

[00:00:33]Right? So suppose for your understanding I'm taking two right angle triangle so that it will be very clear what I'm trying to tell you. Okay. So trigonometry is the relationship between as I told you it's a relationship between the sides and angle of a right angle triangle. So suppose this is a triangle which is a b c and this is another triangle which is a b c I mean to say or the same triangle doesn't matter. Okay. Now you know this angle is 90° correct for both of them. This is 90. This is also 90. But now let's talk about the sides.

[00:01:20]So side opposite to 90° is hypotenous.

[00:01:25]Okay. So here it is hypotenus. Here it is hypotenus as well. Correct? Because both are opposite to 90°. But you know what is perpendicular and where is base?

[00:01:37]So generally people think this is perpendicular and this is base. Correct?

[00:01:43]Not wrong. Okay. But do you know when it is perpendicular? If the considered angle will be theta I'm going to say if I'm considering this angle then the opposite of this angle will be perpendicular and this will be base. But if I'm considering this angle correct as theta then opposite so I'm making it in a different color suppose it is v theta I'm considering this angle as theta right okay then opposite to this angle this one will be perpendicular and this one will be base correct this means the perpendicular and base changes depending on the considered angle okay this is the first so in this case hypotenus is a c a c or a c and perpendicular is ab and base is bc correct but in this case the perpendicular is bc hypotenus is always as it is ac o opposite to 90 but the base is which one am I right so this you need to keep it in your mind. So this is two different scenario.

[00:03:00]Okay. Now we also know the Pythogus theorem which will be applied to all right angle triangle and the theorem is that hypotenus square equal to perpendicular square plus basis square.

[00:03:17]So from this formula we can find all the hypotenus perpendicular and basis. If any of the two is given I can find the third one. like I'm writing them separately that hypotenus equal to roo<unk> over perpendicular square + b square base= to roo<unk> over hypotenus square minus perpendicular square and perpendicular equal to roo<unk> over hypotenus square minus base square okay so this is the basic properties of a right angle triangle now what is the special integonometry so let us think integonometry We understand the ratio between the sides of a trigonometrical ratio between the sides of a right angle triangle. So what you can say what are the possible ratio? You think the possible ratios can be perpendicular by hypotenus. It can be base by hypotenus. It can be perpendicular by base. It can be base by perpendicular. It can be hypotenous by base. or it can be hypotenous by perpendicular. So these are the six possible ratio out of this perpendicular base and hypotenus and these ratios are said to be six trigonometrical terms which are called sine.

[00:04:45]Then another one is cos then the third one is 10. Then we have cot. Then we have se and then we have cosec but you know perpendicular and basis are dependent on theta. This means sign will be meaningless without the angle. So which angle I'm talking about? Suppose this is theta here. So I'm talking about this theta in this case and in this case this theta I'm talking about. So sin theta this will be cos theta it will be tan theta. Theta is nothing but theta is a symbol of angle right. Okay. So c theta se theta and cosec theta.

[00:05:29]Now from where this terms comes up. So these are the short form of sine and this is cosine.

[00:05:40]This is tangent.

[00:05:44]This is coangent.

[00:05:49]This is second and this is co-second and from this I have like we have taken first three character like sine cos tan cot sec but what happened here if I'll be taking three character then pronunciation is almost same to cos if I'll be taking four character still the pronunciation is almost same to cos that's Why we have taken three character five character instead of three character so that it will be cosec co.

[00:06:27]Okay. So this is all about the trigonometrical ratio. So these are called trigonometrical ratio.

[00:06:39]Now generally people used to forget about this perpendicular hypotenus. This ratio they usually forget. So what I'm doing I can give a short way to remember have a look this sign this sign is reversed with this cosec okay like perpendicular by hypotenus and this is hypotenous by perpendicular this cause is reverse with this sec have a look it is base by hypotenus then is hypotenus by base and this 10 is reverse with this cord like perpendicular by base and that is again base by perpendicular correct.

[00:07:22]So we can consider that these two are reverse to each other. These two are reverse to each other and these two are reversed to each other. So they are reversed or reciprocal to each other. Correct?

[00:07:40]So to so you can say simply that sin if I'm writing somewhere sin theta it can be 1x cosec theta or cosec theta can be 1x sin theta am I right? Similarly the cos theta can be reverse of se theta right. So you can say that cos theta is the reverse of se theta. Similarly tan theta will be reverse of cot theta.

[00:08:13]Okay. Now as I told you it will be it will be memorizing first three rest of the three will be memorized because they are reverse to each other. Correct? So I'm going to tell you a trick to memorize the first three. So look at this one which I'm going to write down like I'm writing sin equal to okay perpendicular by hypotenus cos = base by hypotenus and tan = perpendicular by base correct so what I can do I'm converting into a phase so that you can remember it properly like that is sum Some people Some people have curly brown hair turned purely black.

[00:09:22]Fine. So it will be if you'll be memorizing this one some people have curly brown hair turn purely black then what you can do you can understand that sine equal to perpendicular by hypotenus cos equal to base by hypotenus and tan equal to perpendicular by base. You can like repeat this sentence two three times and then you can memorize it very easily and this whole part will be automatically memorized. Okay.