Inverse functions (1 Viewer)

[micuzzo]

^can u explain in more detail plz

 

[Trebla]

y = sin x is a function as it passes the vertical line test (for every x there is only one y). However it fails the horizontal line test, which implies that for every y-value there are multiple x-values.

This means the inverse relation (where you swap x and y) has multiple y-values for every x-value (notice this is swapping x and y from bold statement).

For it to be an inverse FUNCTION (a function has one y-value for every x-value), you have to restrict the domain for y = sin x, say -π/2 ≤ x ≤ π/2. This is equivalent to restricting the range of y = sin^-1x to -π/2 ≤ y ≤ π/2. Therefore we can have an inverse FUNCTION in the given restrictions because the 1-1 property exists. If we did not restrict it, there would be no 1-1 correspondance between x and y.

 

[Timothy.Siu]

ok i get that... just not wher to put it... can u do tan[arcsin(-root3/2)]

i no i can do with calc... just working confusing

u can use a triangle...2 is the hypotenuse and -root3 is a side so the other side must be 1,

so tan(-root3/1)=-60

 

[micuzzo]

y = sin x is a function as it passes the vertical line test (for every x there is only one y). However it fails the horizontal line test, which implies that for every y-value there are multiple x-values.

This means the inverse relation (where you swap x and y) has multiple y-values for every x-value (notice this is swapping x and y from bold statement).

For it to be an inverse FUNCTION (a function has one y-value for every x-value), you have to restrict the domain for y = sin x, say -π/2 ≤ x ≤ π/2. This is equivalent to restricting the range of y = sin^-1x to -π/2 ≤ y ≤ π/2. Therefore we can have an inverse FUNCTION in the given restrictions because the 1-1 property exists. If we did not restrict it, there would be no 1-1 correspondance between x and y.

thanks heaps... that makes it very clear... i cant believe its that obvious

u can use a triangle...2 is the hypotenuse and -root3 is a side so the other side must be 1,

so tan(-root3/1)=-60

yer ok ill figure it out thanks

 

[micuzzo]

... a new day a new challenge...

can someone plz do

show that
arctan 4 - arctan 3/4 = pi/4


and



how would i show if y=sinx and y=arcsinx is an odd or even function.

 

[kurt.physics]

how would i show if y=sinx and y=arcsinx is an odd or even function.

I think you would do the same thing you would do for normal functions, ie use

if f(x) = f(-x), then f(x) is even and;

if f(-x) = -f(x), then f(x) is odd.

for y = sinx

sin(-x) = -sin x = -(sinx),

hence y = sinx is odd.

 

[micuzzo]

^ i forgot about tht.. and ive forgotten trig.... 4 which ratios will ratio (-x) = -ratio(x)

 

[kurt.physics]

^ i forgot about tht.. and ive forgotten trig.... 4 which ratios will ratio (-x) = -ratio(x)

what you need to know is ASTC, and that positive angles are read anti-clockwise on the unit circle, and negative angles are measured clock-wise on the unit circle. So you could just figure it out through that

 

[micuzzo]

what you need to know is ASTC, and that positive angles are read anti-clockwise on the unit circle, and negative angles are measured clock-wise on the unit circle. So you could just figure it out through that

u can but theres easier way to do it whihc i did today lol

thanks for help