# Sketching Inverse Trig Functions of Functions (1 Viewer)

#### SunnyScience

##### Member
Can someone please explain to me how to answer the following questions please Sketch the graphs of the following functions:
i. y = cos^-1(cosx)
ii.y = cos(cos^-1x)
iii.y= tan^-1(tanx)

How do you determine the domain and range of these functions, as well as there shape?

thank you. #### Sanjeet

##### Member
they're all y=x ?

#### zeebobDD

##### Member
they're all y=x ?
nope, there y=x from a specific point to another

#### Skeptyks

##### Member
II: Draw the straight line y = x with domain -1 <= x <= 1, range -1 <= x <=1. <= means less than equal to btw.
III: Draw the straight line y = x with domain -pi/2 <= x <= pi/2 and range -pi/2 <= x < pi/2.

I don't know if this explanation is 100% correct but here it goes... y=cos^-1x has a domain of -1 <= x <= 1 and if you go cos^-1x(cosx), they simply cancel each other out and leave you with x, giving you the equation y =x and a domain as stated above. Similarly true for tan^-1x.

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#### SpiralFlex

##### Well-Known Member
This may or may not help you. (Sketching other graphs) This was posted by me a long time ago. I sent this to someone so they could explain it to a friend.

SpiralFlex said:
Hello, sorry I was having a fun day out. Sorry for late reply. This is how I would explain it.