- #1

determine the # of solutions to the equation...

sinax=b

for the domain 0 (less than or equal to) x (less than or equal to) 2pi, for the values of a. a is a pos. integer and b is a real #.

Then it gives examples:

value of a ... value of b

...1 ... ... 0

... 2 ... ... 0.2

...3 ... ... -0.2

... 4 ... ... 1

...0.5 ... ... 0.5

... 1 ... ... 2

MY ANSWER:

sin (ax) = b

From a = 1 and b = 0:

sin x = 0

x = {0, pi, 2(pi)}

From a = 2 and b = 0.2:

sin (2x) = 0.2

2x = approximately {0.2014, 2.9402, 6.4845, 9.2234}

x = approximately {0.1007, 1.4701, 3.2423, 4.6117}

From a = 3 and b = -0.2:

sin (3x) = -0.2

3x = approximately {3.3430, 6.0818, 9.6261, 12.3650, 15.9093, 18.6482}

x = approximately {1.1143, 2.0273, 3.2087, 4.1217, 5.3031, 6.2161}

From a = 4 and b = 1:

sin (4x) = 1

4x = {(1/2)(pi), (5/2)(pi), (9/2)(pi), (13/2)(pi)}

x = {(1/8)(pi), (5/8)(pi), (9/8)(pi), (13/8)(pi)}

...But I am not sure how to explain what I did out. And also, I didn't do the last two options, because they messed me up.

Can anyone help?

I need help.