Question

sin-¹(-1/2)

the answer is -π/6
how do I get that answer?

Answer 1

We have
\[\sin^{-1} (-1/2)\]?
do you know the range of \(\sin^{-1} x\)?

Answer 2

Are you here @SandyHearts ?

Answer 3

All it says is find the exact value of each expression. No range or anything.

Answer 4

I know that but do you know about \(\sin^{-1} x\)?

Answer 5

no i do not

Answer 6

Do you want me to tell you about it? then the problem will be solved in seconds!!

Answer 7

yes, of course.

Answer 8

oh wait the anser is -π/6

Answer 9

I just don't know how to get it.

Answer 10

Ok, I'll explain you. You know sin x?

Answer 11

what about it?

Answer 12

What is the range of sin x? I mean what's its minimum value and what is its maximum value?

Answer 13

0-180? i have no idea

Answer 14

You know when
\[x =0\longrightarrow \sin x =0\]
\[x =\pi/2\longrightarrow \sin x =1\]
\[x =-\pi/2\longrightarrow \sin x =-1\]
Do you get this?

Answer 15

yes I get this. Like in the unit circle.

Answer 16

Yeah, so sin x max value is 1 and min value is -1

Answer 17

You know the inverse of sin x is \(\sin^{-1}x\)
Just like division is inverse of multiplication
We multiply x by 2 and divide it by 2, we'll get back x
Do you get this?

Answer 18

You know sin x repeats its value after \(2\pi\)?
So we have fixed the range and domain of \(\sin^{-1} x\)
\[ \text{x can only be between -1 and 1}\]
\[\text{and its range is from }\frac{-\pi}{2} \text {to}\frac{\pi}{2}\]
Do you get this?

Answer 19

yes

Answer 20

Ok tell me at what value of x , sin x =1/2?

Answer 21

sin-¹(1/2)=x @ash2326

Answer 22

I mean
When \(x=60\ \sin x=\frac{\sqrt 3}{2}\)
so for what value of x, sin x=1/2, check your unit circle and tell

Answer 23

π/6 ?

Answer 24

Yeah:D you're right so tell me know
\[\sin^{-1} (-\frac{1}{2})=?\]

Answer 25

-π/6

Answer 26

Yay:D did you understand it?

Answer 27

Yes, thank you so much!

Answer 28

Welcome:D