Inverse Sine of Sine

[markoj]

Thank you! Your explanation is perfect. After 16years of studying and working as an engineer, I did not know about that.

[luisclementeortegasegovia]

Professor you always surprise us with new approches!

[vinay__sn]

I am from India, I wish I had a teacher like you in my school

[ursulapainter]

Thank you very much! Your dedication is highly appreciated.

[pde]

I like the teacher like you and should be more like u.

[aarush_rockz]

you can also wite it as pi-x. If the number in between pi/2 and 3pi/2( like over here). This is inferred from its graph.

[btsmochimi]

You're saving my calculus grade...thank you sir❤

[HaldaneSmith]

sin-1(sin(x)) = x or (pi - x) depending on the value of x. I think.

[beutyindetail]

i did not know that. thank you sir very much.

[ANIMX_FLAME]

I am a grade 9 student but how do we cancel out the sine because in normal trigonometry (not inverse ) we dont fo that i guess

[Broadsmile]

It's an interesting problem, because sine is periodic, but has a period of 2π or τ, and arcsine is periodic, but has a period of π. Could be solved for any input value without trig tables abs(mod(x-90°, 360°)-180°)-90°

[levyroth]

This part of math is like gibberish to me 😂

[jernall]

Can you do some examples of spherical trigonometry, it would help me a lot, thanks.

[farhansyabibi]

Why is cos(60°) = 1/2 and cos(-60°) = 1/2
But cos-1(1/2) is only 60° and not -60° ??

[AdoshMotilall]

Thank you for explaining how to solve this problem. I do although have one question. How were you able to get 1/2 if sin(5pi/6) equals to 0.04567671501? Was there specific formula to get to 1/2? That’s where I got lost. Is it possible to explain the solution in terms of where you got the 1/2 from?

[swap]

Hello I saw this in a physics book:

Tan(alpha)= x
Implies that
Alpha= tan^-1(x)

Really, is this true, is tan alpha or tan theta the product of tan and theta/ tan × alpha. ???

Note there was a big quantity representing x here

[Sgth]

So this is why you replied to me that day. I forgot about the range of sine... well the domain of sine inverse

[phillipchen]

does this limitation also apply to cos

[Fe-lqwn]

But just some info if we take matters to the complex world then one if the many possible answer is indeed 5π/6

[ahmedrizk]

I don’t think your answer is correct as multiplications of pi as an angle still gives the pi