Christmas MT's answer to :^)'s Secondary 4 A Maths Singapore question.
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This question is testing the fundamentals properties of sine/cosine waves.
To find least/greatest values, u will need to have the amplitude. For a basic sinx or cosx, amplitude is 1 so their least/greatest values are -1 and 1.
For f(x), amplitude is 2 since it is 2sin instead of just a sin. So least value is -2 and greatest is 2.
For g(x), amplitude is 3 using similar approach to f(x). However, g(x) has a -1 in the equation thus least value is -1-3=-4 and greatest value is -1+3=2.
Period is the full cycle of a sinx/cosx which is 2pi.
For f(x), it is sin2x instead of sinx, so period here is 2pi/2=pi.
For g(x), it is cos(x/2) instead of cosx, so period here is 2pi/(1/2)=4pi.
To find least/greatest values, u will need to have the amplitude. For a basic sinx or cosx, amplitude is 1 so their least/greatest values are -1 and 1.
For f(x), amplitude is 2 since it is 2sin instead of just a sin. So least value is -2 and greatest is 2.
For g(x), amplitude is 3 using similar approach to f(x). However, g(x) has a -1 in the equation thus least value is -1-3=-4 and greatest value is -1+3=2.
Period is the full cycle of a sinx/cosx which is 2pi.
For f(x), it is sin2x instead of sinx, so period here is 2pi/2=pi.
For g(x), it is cos(x/2) instead of cosx, so period here is 2pi/(1/2)=4pi.
Date Posted:
3 years ago
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