中五MATHS

1. Period = 360/10 = 36 degree. B
2. Period = 360/3 = 120 degree. C.
3. Period = 360/1 = 360 degree. D,
4. Period = 360/2a = 60, so a = 3. C.

1.
The period of the function g(x) = cos(x) is 360度
The period of the function f(x) = cos(10x) is 360度/10=36度 Ans: B. 36度2.
The period of function g(x) = sin(x) is 360度
The period of function f(x) = sin(3x+30度) is 360度/3=120度 Ans: C. 120度3.
The period of the function g(x) = sin(x) is 360度
The period of the function f(x) = -2+4sinx is 360度 Ans: D. 360度 4.
the period of the function g(x) = sin(x) is 360度
the period of the function f(x) = 3sin(2ax)+4 is 360度/(2a) 360度/(2a)=60度
360度=60度*(2a)
6=2a
a=3 Ans: C. 3

General method for these questions: if T is the period of the function f(x)=a*sin(bx+c)+d,
we have
f(x+T)=f(x)
a*sin(b(x+T)+c)+d=a*sin(bx+c)+d
a*sin(bx+bT+c)+d=a*sin(bx+c)+d
a*sin(bx+bT+c)+d=a*sin(bx+c)+d
sin(bx+bT+c)=sin(bx+c)Since the period of the function g(x)=sin(x) is 360度,
bx+bT+c=bx+c+360度
bT=360度
T=(360度/b)So, we can see that the period of the function f(x)=a*sin(bx+c)+d
is only affected by the coefficient of x,i.e. b.