Q: express 3sin+4cos in the form Rsin(theata + alpha). And 0< alpha < 90 degrees
(!)= theata
(?)= alpha
ii) hence, solve the equation 3sin(!) + 4cos(!) +1 = 0
solutions between -180 and 180
Ive done part1 which gives the angle 53.1.....
the he second part I'm stuck with as I don't think I'm correct, here is my working out for part 2
3sin(!) +4cos(!) = inverse tan(4/3)
therefore re can I just make it
tan = 4/3 -1
inverse tan = 18.4349.....
i have no clue what I'm doing thus me guessing what to do...
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ADotCross
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- 04-12-2014 16:55
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- 04-12-2014 17:05
(Original post by ADotCross)
Q: express 3sin+4cos in the form Rsin(theata + alpha). And 0< alpha < 90 degrees
(!)= theata
(?)= alpha
ii) hence, solve the equation 3sin(!) + 4cos(!) +1 = 0
solutions between -180 and 180
Ive done part1 which gives the angle 53.1.....
the he second part I'm stuck with as I don't think I'm correct, here is my working out for part 2
3sin(!) +4cos(!) = inverse tan(4/3)
therefore re can I just make it
tan = 4/3 -1
inverse tan = 18.4349.....
i have no clue what I'm doing thus me guessing what to do... -
ADotCross
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- 04-12-2014 17:21
Yes, just flicking through them
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fossilcollective
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- 04-12-2014 17:31
(Original post by ADotCross)
Q: express 3sin+4cos in the form Rsin(theata + alpha). And 0< alpha < 90 degrees
(!)= theata
(?)= alpha
ii) hence, solve the equation 3sin(!) + 4cos(!) +1 = 0
solutions between -180 and 180
Ive done part1 which gives the angle 53.1.....
the he second part I'm stuck with as I don't think I'm correct, here is my working out for part 2
3sin(!) +4cos(!) = inverse tan(4/3)
therefore re can I just make it
tan = 4/3 -1
inverse tan = 18.4349.....
i have no clue what I'm doing thus me guessing what to do...
Rsin(θ + 53.1) = -1 (using the value you calculated for R)Last edited by fossilcollective; 04-12-2014 at 17:37. -
ADotCross
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- 04-12-2014 17:44
So it would be
inverse tan-1/5 - 53.1.... Then makes missing theata number ? -
davros
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- 04-12-2014 19:48
(Original post by ADotCross)
So it would be
inverse tan-1/5 - 53.1.... Then makes missing theata number ?
You have an equation that is basically
sin(something) = something else
so the first thing you should be doing is an inverse sine! -
ADotCross
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- 04-12-2014 21:06
Sin(theata +53.1) = -1/5
can I then inverse sin to make
theata + 53.1 = inverse sin(-1/5)
then - 53.1
theata = -64.63...
is is that how you do it ? -
davros
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- 04-12-2014 21:17
(Original post by ADotCross)
Sin(theata +53.1) = -1/5
can I then inverse sin to make
theata + 53.1 = inverse sin(-1/5)
then - 53.1
theata = -64.63...
is is that how you do it ?
(and it's theta by the way)
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ADotCross
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- 06-12-2014 16:14
Yh I got the rest thanks, I found the angles between the range.
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