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Well, I'm a little stuck on this question, A-level standard (P1).
Find all the solutions of the equation
sin(3x + 45 degrees) = 0.7
in the interval -90 degrees ¡Ü x < 90 degrees, giving your answers to teh nearest 0.1 degree.
I got the primary solution of -0.2 but I am stuck on how to get the other 5 solutions.
Find all the solutions of the equation
sin(3x + 45 degrees) = 0.7
in the interval -90 degrees ¡Ü x < 90 degrees, giving your answers to teh nearest 0.1 degree.
I got the primary solution of -0.2 but I am stuck on how to get the other 5 solutions.
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i only just started doing this topic yesterday and so only on the f(X) things, but i'll give it a shot (it'll probally be wrong as its based on my knowledge of gcse)...
sin(3X + 45) = 0.7
let 3X + 45 = $
sin $ = o.7
but as 3X + 45 = $ , if -90 < X < 90 ,
then (3x (-90) + 45) < 3X +45 < (3x (90) + 45) so -255 < X < 315
so now the problem has become sin $ = o.7 with -255 < X < 315
inverse sin (o.7) = 44.4
another root is -44.4
-44.4 - 180 = -224.4
-44.4 + 180 = 135.6
44.4 - 180 = -135.6
44.4 + 180 = 224.4
so therefore the roots of sin $ = o.7 with -255 < X < 315 are:
-224.4 , -135.6 , -44.4 , 44.4 , 135.6 , 224.4
returning to the orginal equation , and using the fact that $ = 3X + 45
the roots are:
-59.8 , -30.2 , - 0.2 , 0.2 , 30.2 and 59.8
but hey, what do i know about trig graphs?
sin(3X + 45) = 0.7
let 3X + 45 = $
sin $ = o.7
but as 3X + 45 = $ , if -90 < X < 90 ,
then (3x (-90) + 45) < 3X +45 < (3x (90) + 45) so -255 < X < 315
so now the problem has become sin $ = o.7 with -255 < X < 315
inverse sin (o.7) = 44.4
another root is -44.4
-44.4 - 180 = -224.4
-44.4 + 180 = 135.6
44.4 - 180 = -135.6
44.4 + 180 = 224.4
so therefore the roots of sin $ = o.7 with -255 < X < 315 are:
-224.4 , -135.6 , -44.4 , 44.4 , 135.6 , 224.4
returning to the orginal equation , and using the fact that $ = 3X + 45
the roots are:
-59.8 , -30.2 , - 0.2 , 0.2 , 30.2 and 59.8
but hey, what do i know about trig graphs?
Peter Venkman wrote:
> Well, I'm a little stuck on this question, A-level standard (P1).
>
>
> Find all the solutions of the equation
>
> sin(3x + 45 degrees) = 0.7
>
> in the interval -90 degrees ¡Ü x < 90 degrees, giving
> your answers to teh nearest 0.1 degree.
>
>
> I got the primary solution of -0.2 but I am stuck on how to get the
> other 5 solutions.
Um if it is sin then you will need to have the first answer minus 180, so 180 - negative 0.2, will be 180.2. then you add 180 to 180.2, then keep going by adding 180 to the answers until you have 5 of them.
> Well, I'm a little stuck on this question, A-level standard (P1).
>
>
> Find all the solutions of the equation
>
> sin(3x + 45 degrees) = 0.7
>
> in the interval -90 degrees ¡Ü x < 90 degrees, giving
> your answers to teh nearest 0.1 degree.
>
>
> I got the primary solution of -0.2 but I am stuck on how to get the
> other 5 solutions.
Um if it is sin then you will need to have the first answer minus 180, so 180 - negative 0.2, will be 180.2. then you add 180 to 180.2, then keep going by adding 180 to the answers until you have 5 of them.
That's what I thought but I got 7 answers and the question is out of 6 marks, one mark for each solution. Oh well.
Having not read your question too well, I *think* all you do is get the answers as usual (but get answers up to 1080 degrees because of the 3x), then re-arrange the equation so you take 45 off the answer, then divide by three...
Thats what I'd do anyhoo.
And this monkey has indeed gone to heaven.
Thats what I'd do anyhoo.
And this monkey has indeed gone to heaven.
All Schoolteachers take crack
oh god i hated this crap. Its where you gotta go round the 4 quadrants on the axis innit? ASTC. All sausages turn cold.
Why'd you laugh?
i just laugh at your kind.
I guess no one knows then.
this monkey has gone to heaven
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