-1< or equal to sinx < or equal to 1. Use this to determine the range

Question

1) y= 2sinx 2) y= (sinx) ^2 3) y= 2^sin(x) 4) y= 1/sinx

Answer 1

1) y= 2sinx

-2<= 2sinx<=2

Since the range of sinx is between -1 and 1, so doubling it will also double the range

2) y= (sinx) ^2

-1<=(sinx) ^2<=1

1^2 is 1. so squaring the function whose range is between [-1,1] wont change the range. this wouldn't be true if the range were bigger than [-1,1] interval.

3) y= 2^sin(x)

Maximum value of sin(x) is when x = (4n+1)pi/2 and the value is 1. so 2^1 = 2 maximum value

Minimum value of sinx is when x = (4n-1)pi/2 and value is -1. so 2^-1 = 0.5

So the range is 0.5<=2^sinx<=2

4) y= 1/sinx

1/sinx = cosec(x)

and range of cosec(x) = R - (-1,1)

or

(-∞,-1) U (1,∞)