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# simple/hard trig. Q help watch

1. Sinsquared X ≥ 1/4
(0<x<360)

can anyone solve this?^o)

thought of doing : sinX ≥ √1/4
but its wrong.
2. (sinx)^2 >= 1/4
sinx >= 1/2
If you draw y = sinx, the curve is above 1/2 between 30 and 150, so:
30 <= x <= 150
3. sinx ≥ 1/2 and -1/2 ≥ sinx

150 ≥ x ≥ 30 and 330 ≥ x ≥ 210
4. (Original post by Dez)
(sinx)^2 >= 1/4
sinx >= 1/2
If you draw y = sinx, the curve is above 1/2 between 30 and 150, so:
30 <= x <= 150
youve forgotten the negative root of 1/4
5. Edit: Wow, beaten to the post by the world and his goat - carry on
6. Whoops, forgot the negative one :P

Edit: And beaten to the realisation too
7. teacher stated that cannot simply take sqaureroot of 1/4 and therefore cannot do:
sinX > +-1/2
8. Why not?
9. (Original post by shah)
teacher stated that cannot simply take sqaureroot of 1/4 and therefore cannot do:
sinX > +-1/2
sin2(x) >= 1/4

Using identity: ½(1-cos(2x) = sin2(x)

-> ½(1-cos(2x) >= 1/4
-> 1-cos(2x) >= ½
-> cos(2x) >= ½
-> x >= ½arccos(½)
10. duno why hoping someone here could answer that. lol
11. (Original post by shah)
teacher stated that cannot simply take sqaureroot of 1/4 and therefore cannot do:
sinX > +-1/2
sin2(x) >= 1/4

Using identity: ½(1-cos(2x)) = sin2(x)

-> ½(1-cos(2x) >= 1/4
-> 1-cos(2x) >= ½
-> cos(2x) =< ½
-> x =< ½arccos(½)
12. thnks for tht.
is there an specific identity as : ½(1-cos(2x)) = sin2(x) ?
or is that wrked out from sin^2x + cos^2x=1.
b'cause this is a C2 Q.?
13. (Original post by shah)
thnks for tht.
is there an specific identity as : ½(1-cos(2x)) = sin2(x) ?
or is that wrked out from sin^2x + cos^2x=1.
b'cause this is a C2 Q.?
If it's a C2 question then the 2nd post is correct. You just square root the RHS and take arcsin of that.

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