- #1
hamface
THE QUESTION:
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.
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.