Question

Evaluate the following. Answers must be in EXACT VALUES!!!
sin^(-1)⁡(sin⁡〖-135°〗 )

Answer 1

So start with sin⁡〖-135°〗
BTW, fancy brackets!!

Answer 2

hhehe

Answer 3

look at your Unit Circle
what's the sine of say 90 degrees?

Answer 4

im confused about what you are asking

Answer 5

i know im in the third quadrant

Answer 6

well.... if you look at your Unit Circle... what does it show for sine of 90 degrees?

Answer 7

just as an example for that matter

Answer 8

why are we looking at 90 degrees

Answer 9

its 1

Answer 10

There is another way: it has to do with the meaning of inverse functions.
sin^(-1) and sin are inverse functions, so they cancel out.

In general, if f and g are each other's inverse, this is what happens if you apply them one after the other:

f(g(x))=x, so NOTHING happens!

Now what do you think is the answer of your question?

Answer 11

so the answer is sin-135?

Answer 12

whatever that value is?

Answer 13

m terrible with trig im reliving a nightmare that i already lived in high school. but i am doing great in statistics...

Answer 14

hhaha

Answer 15

I understand your troubles!

In this case, the problem is not so straightforward, because of the value -135.
That is why you have to draw a unit circle. Here is one:

Answer 16

i get the picture

Answer 17

The value of sin(-135) is the same as sin(-45), as you can see in the image.
Therefore, if you apply sin^-1, you don't get -135 back , but -45, because that number is closer to 0.

Answer 18

okay that makes sense

Answer 19

It is caused by the way sin^-1 is defined. It means you alway get back to angles between -90 and 90 degrees, by the same reasoning as above.

Answer 20

okay thank you for helping me. my daughter woke up and i have to take care of her now.

Answer 21

Take care of her, it is more important than maths!