Small angle approximations for sin(x), cos(x) and tan(x) : ExamSolutions Maths Revision

[@shashankrai1204]

Thanks dude...Was stucked in derivation of refraction due to spherical surfaces where this was used. Thanks again buddy...You saved my day🌷💯💯

[@DdoubleB03]

Very interesting proof. Thank you!

[@qimingtian]

Thank you so much!!!! such a great video

[@sohamroy474]

I totally understood the proofs. But when I am actually trying 'em on the calculator, I am not able to verify. For example, if I google tan3, it says -0.14... which is not even close to 3. What exactly am I doing/understanding wrong?

[@aidantransitus9585]

This is only true for small angles, 3 radians is not that small of an angle (around 172 degrees). Generally if x

[@Prathum01]

up to which angle can each of these be used pls help

[@Anjalikumari-ex2db]

Thank you sooo much .

[@ExamSolutions_Maths]

That's okay. Pleased it helped.

[@algobrax]

thank you!

[@kirilljohnson2474]

Could you please advise on what would be an approximation for cos 3 theta?

[@isaacjacobharris]

1- (9*theta^2)/2

[@akhilesh1466]

Thanks

[@Wowow10000]

Thanks helpfull

[@theodoresweger4948]

MY big mistake not using radian mode in my HP 35s now works out great..

[@trollghostol]

couldnt you just look at the graph of sin(x) and tan(x) and see that their gradient approaches 1 at x=0?

[@ExamSolutions_Maths]

+Ell “christkidz” Op How does that show that sin(x) is approx x, tan(x) is approx x and cos(x) is approx 1-(x)^2/2

[@trollghostol]

ExamSolutions well, if the gradient approaches one, the tangent to the graph as x approaches 0 is nearly y=x, and since y is sin(x), it shows that sin(x) is approximately x, same with tan, although it dont know how it would work with cos(x) sorry

[@ExamSolutions_Maths]

+Ell “christkidz” Op There are several ways to prove this these results as I said at the beginning, this was just one way.

[@harveywalters8620]

xxx

[@takyc7883]

I prefer using the derivative proof