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# domain and range of sin, cos and tan watch

1. Would the domain of cos and sin be 360, and the range -1 < f(x) < 1 ?
If so, how would it change if f(x) was 2cos-1(x -1)
2. (Original post by Mark Scicluna)
Would the domain of cos and sin be 360, and the range -1 < f(x) < 1 ?
yo

Do you understand the definition of domain and range first?
3. edit: if the functions are restricted so an inverse exists then the following is true

domain of sin: -90 to 90
domain of cos: 0 to 180
4. yeh i do, isnt the domain all possible inputs (x coordinates), and the range is all possible outputs (y coordinates)
5. thnx, that really helps
6. (Original post by haarithiop)
Domain of sin is -90 to 90, domain of cos is 0 to 180. Domain is values you can put in, for sin to be a one to one function (for every x value theres one y value) then you can only put values of -90 to 90 in to get out the values from -1 to 1. With cos you put in values 0-180 to get values 1 to -1 out.
(Original post by Mark Scicluna)
yeh i do, isnt the domain all possible inputs (x coordinates), and the range is all possible outputs (y coordinates)
And for tan it's also between -90 and 90 degrees
7. Not sure what the other posts here are on about, I think they're under the belief that arcsin is the inverse of sine etc. The domain of sine and cosine is the set of real numbers, whereas tan has discontinuities, which you can see from the graph above, that you should account for.
8. (Original post by Mark Scicluna)
Would the domain of cos and sin be 360, and the range -1 < f(x) < 1 ?
If so, how would it change if f(x) was 2cos-1(x -1)
What does a domain of 360 mean?

The domain is (if not restricted) the set of x values where a function f is defined. Sinx and cos x have domains which are the set of real numbers, you can see this if you draw the graphs which are periodic.

And tan x isn't defined for odd multiples of pi/2 rads.

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