Question

Hey! So im learning Inverse of trig functions in school, so can anyone please explain them to me? I was absent in class and I have no idea on how to even attempt the problem, heres how to do it but can someone explain why? Thank you in advance! :)
Sinx + 1 = 0

Answer 1

do you know what an inverse function is spose to do to begin with?

Answer 2

yes :)

Answer 3

good, inverse trig functions are the result of restricting the domain of thier normal trig function

Answer 4

Sinx + 1 = 0

first thing you would want to do is get sinx all by itself; how would we do that?

Answer 5

bring it to the other side so sinx = -1

Answer 6

correct, and all that is left is to inverse the trig function, on both sides, to get the x out

Answer 7

arcsin(sinx) = arcsin(-1)

x = arcsin(-1)

Answer 8

thats where i am confused! :/

Answer 9

can you explain that?

Answer 10

let's say there is a function y=sin x , then expressing y in terms of x means inverse of it ,
which is\[x= \sin ^{-1} y\]

Answer 11

trig functions take angles as inputs and give ratios as outputs; the inverse trig functions therefore take in ratios and give out angles.

Answer 12

if you know what an inverse function is, then there isnt much mystery to trig inverses.

Answer 13

but the attachment i put above is the answer

Answer 14

sinx=-1 is asking, what angles give us a sin ratio of -1

x = arcsin(-1) is asking or telling us the same thing; x equates to all the angles that have a sin ratio of -1

Answer 15

youre most likely confused at why the answer is given in terms of more than one angle then?

Answer 16

how did they get 3/2 ?

Answer 17

can you give me one single angle that has a sin ratio of -1?

Answer 18

3pi/2 is a radian measure that corresponds to 270 degrees

Answer 19

radians are the prefered means of working with trig functions

Answer 20

2pi = 360 degrees

270 is 3/4 of 360 degrees

2pi * 3/4 = 3pi/2

Answer 21

its \[\frac{ 3 \pi }{ 2 }\] sorry amistre to interrupt you :)

Answer 22

no problem, by all means i usually need interupting just to keep meself inline ;)

Answer 23

:)

Answer 24

since 3pi/2 is one angle that has a sin ratio of -1; and all angles that periods of 2pi from it have the same sin ratio; we can include all of the angles by adding on that little 2pi k part. where k is any integer

Answer 25

it like saying the x^2 = 4 has the solutions +- 2

Answer 26

but how is 3pi/2 an angle that has a a sin ratio of -1?

Answer 27

what is the sin of 270?

Answer 28

270 degrees that is