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# inverse trig question watch

1. here is question

2. where that 2 goes

i know first to take inverse of sin sqroot 2/2
then what to do of 2 with that?
3. (Original post by Qer)

where that 2 goes

i know first to take inverse of sin sqroot 2/2
then what to do of 2 with that?
sin(2x) = 2 cos x sin x
4. (Original post by Zacken)
sin(2x) = 2 cos x sin x
can you please show me working?. it will be easier for me to understand
5. (Original post by Qer)
can you please show me working?. it will be easier for me to understand
No. Tell me what you've done so far. What is arcsin(sqrt(2)/2)? What is 2 times that? What is sin of that?
6. (Original post by Zacken)
No. Tell me what you've done so far. What is arcsin(sqrt(2)/2)? What is 2 times that? What is sin of that?

is it like that
2 arcsin sqroot 2/2= 2 X 1/4pi = 1/2 pi
sin( 1/2 pi)=1

not sure that it is right?
7. (Original post by Qer)
is it like that
2 arcsin sqroot 2/2= 2 X 1/4pi = 1/2 pi
sin( 1/2 pi)=1

not sure that it is right?
It is. See, all you had to do was try it yourself.
8. (Original post by Zacken)
It is. See, all you had to do was try it yourself.

can i ask some more questions?
9. (Original post by Qer)

can i ask some more questions?
Sure. As long as you lay out your current working/thoughts for them.
10. (Original post by Zacken)
Sure. As long as you lay out your current working/thoughts for them.

so
i am ok with part a . as we can see from graph

for part b
i
cos^2k =1- sin^2k
taking sqroot
cos k= 1- sin k

the book shows answer is +- sqroot(1-sin^2 k)

why they dont cancel sqroot?

part c doesnt make any sense to me
11. (Original post by Qer)

so
i am ok with part a . as we can see from graph

for part b
i
cos^2k =1- sin^2k
taking sqroot
cos k= 1- sin k

the book shows answer is +- sqroot(1-sin^2 k)

why they dont cancel sqroot?

part c doesnt make any sense to me
sqrt(1-sin^2 k) is not the same thing as 1 - sin k.

Do you think that sqrt(1-0.5^2) = 1 - 0.5?
12. (Original post by Zacken)
sqrt(1-sin^2 k) is not the same thing as 1 - sin k.

Do you think that sqrt(1-0.5^2) = 1 - 0.5?
ok
that make sense now
13. (Original post by Qer)
ok
that make sense now
You know that if 0<k<pi/2 then cos k is a positive number, which is why cos k = sqrt(1- sin^2 k)

If -pi/2 < k < 0, what is the sign of cos k? Check a graph. Is it under/below the k-axis in that interval?
14. (Original post by Zacken)
You know that if 0<k<pi/2 then cos k is a positive number, which is why cos k = sqrt(1- sin^2 k)

If -pi/2 < k < 0, what is the sign of cos k? Check a graph. Is it under/below the k-axis in that interval?
how i make graph of function cos k = sqrt(1- sin^2 k)?
15. (Original post by Qer)
how i make graph of function cos k = sqrt(1- sin^2 k)?
No, make a graph of the function cos k.
16. dran
(Original post by Zacken)
You know that if 0<k<pi/2 then cos k is a positive number, which is why cos k = sqrt(1- sin^2 k)

If -pi/2 < k < 0, what is the sign of cos k? Check a graph. Is it under/below the k-axis in that interval?
graph is in second quadrant ( above the axes) so it is positive
17. (Original post by Qer)
drangraph is in second quadrant ( above the axes) so it is positive
Right, so there's no difference to your answer. cos k = sqrt(1 - sin^2 k)

You just need to rewrite sin^2 k in terms of x.
18. (Original post by Zacken)
Right, so there's no difference to your answer. cos k = sqrt(1 - sin^2 k)

You just need to rewrite sin^2 k in terms of x.
there is also tan in par b
is this answer for both of them?
19. (Original post by Qer)
there is also tan in par b
is this answer for both of them?
You tell me. Is tan k positive for 0<k<pi/2? What about for -pi/2 < k < 0?
20. (Original post by Zacken)
You tell me. Is tan k positive for 0<k<pi/2? What about for -pi/2 < k < 0?
Is tan k positive for 0<k<pi/2?
it is positive

-pi/2 < k < 0?
in that range it is below the axes so it is negative?

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