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secondary 4 | A Maths
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And starting my revision
The person never help me out with qns 2
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I will stop for two days.
I will do math on Thursday
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Will do the rest another time.
a sin x + b cos x = R sin (x + alp)
a sin x - b cos x = R sin (x - alp)
a cos x + b sin x = R cos (x - alp)
a cos x - b sin x = R cos (x + alp)
R = sqrt (a2 + b2), essentially Pythagoras theorem
alp = tan-1 (b/a) and must be an acute angle
If the form is R sin (x +- alp), you must put the sin x first before cos x (eg 5 sin x + 2 cos x, not 2 cos x + 5 sin x) as putting the wrong order will get you the wrong order, and hence the wrong angle, for alp.
If the form is R cos (x +- alp), you must put the cos x first before sin x.