1. ## Siren wave

I have done the attached question but I don't entirely understand it. I used degrees but is there any reason to not use radians? How long is the wave period in minutes?

2. I don't think the length of a wave is given or needed. Only percentages of a wave above certain y values are calculated.

3. (a), at least, is very easy: the maximum value of sin(x) is 1 and the minimum value is -1.

For (b), you are asking when 20 sin(6t)+ 70> 75 which is the same as asking when sin(6t)> 5/20= 1/4. Determine the value of 6t (you don't need or want t) for which sin(6t)= 1/4 and check to see which intervals give ">" and which "<". Divide the length of the correct interval by 360 (if you use degrees) or by $2\pi$ if you use radians.

For (c), use the same method as (b) except "in reverse". 45% of 360 is 162 so you want A sin(6t)+ 70= 75, or sin(6t)> -5/A for a difference of 6t= 162(6)= 972 degrees.

4. Yes, I said I'd done the question. I see now I don't need t. I could have used x instead in my working to show that x and t are different.

5. The 6 isn't needed either. Its an unusual question.