math trig problem

[Electrons]

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What is the max value for 2sin(pi+x) + sin(x) + 2?


Answer is 3. How?

 

[TeamGuo]

If you let x = 3xpie/2 you get 3.

2 sin(5xpie/2) + sin(3pie/2) +2 = 2(1) - 1 + 2 = 3

 

[Electrons]

If you let x = 3xpie/2 you get 3.

2 sin(5xpie/2) + sin(3pie/2) +2 = 2(1) - 1 + 2 = 3

Thanks, but how did you come to pick x = 3(pi/2) at first as starting point? Why not other number? How would you start if the choices were:
a) 1
b) 2
c) 3
d) 4
e) 5

 

[TeamGuo]

they wouldn't give you those numbers since it's a trig problem.

I just drew the sine graph and plugged in couple of values such as pie/2 and 3pie/2

Best approach is knowing the trig graphs, then you can eliminate some answers right away.

 

[Electrons]

they wouldn't give you those numbers since it's a trig problem.

I just drew the sine graph and plugged in couple of values such as pie/2 and 3pie/2

Best approach is knowing the trig graphs, then you can eliminate some answers right away.

Actually they did bro but it wasn't in same order as I created.

I guess I just have to try the graph and plug in value like you mentioned.

 

[TeamGuo]

really... hmm... yea the easiest would to graph. Then you know the range of values you get.

 

[Streetwolf]

What is the max value for 2sin(pi+x) + sin(x) + 2?


Answer is 3. How?

The sin function oscillates between -1 and 1 so the maximum value of any given sin function is the amplitude. In this problem you have 2 sin functions. The first has a 2 for an amplitude and the second has a 1. You should note that the period of the first one is shifted by pi. That means the two functions will have opposite signs of the same magnitude. The catch here is that the first one is multiplied by 2 so if you want the max value, you want that one to be positive.

Now you have to think a little. Forget the amplitudes for a moment. You have two functions which will give you the same magnitude of an answer, with different signs. This is sorta like absolute value. Think of some examples: -1 and 1. -2 and 2. -10 and 10. Notice that the HIGHER THE AMPLITUDE, the GREATER the distance between the two. If you added any of these pairs you would get 0. But if you added DOUBLE the positive one to the negative one, your answer would be the positive number (for example 2 and -2 would be 4 + -2 which is 2, which was the original positive number. With 10 and -10 you'd get 20 + -10 which is 10, which was the original positive number.) That means the higher the magnitude, the greater your answer will be.

Taking that into this problem, you'd want to choose the highest possible value of sin(x) which is 1. Since you want the sin function with the 2 amplitude to be positive, you need to come up with x such that sin(pi + x) = 1. But who cares since it wants the maximum of the entire thing (FYI it would be x = 3pi/2 to name one possibility). You KNOW that you'll get 2 for the value of 2sin(pi + x) and you KNOW that you'll get -1 for the value of sin(x). Since the 2 at the end remains constant, you have 2 - 1 + 2 = 3 which is the max value of this expression.

 

[Electrons]

The sin function oscillates between -1 and 1 so the maximum value of any given sin function is the amplitude. In this problem you have 2 sin functions. The first has a 2 for an amplitude and the second has a 1. You should note that the period of the first one is shifted by pi. That means the two functions will have opposite signs of the same magnitude. The catch here is that the first one is multiplied by 2 so if you want the max value, you want that one to be positive.

Now you have to think a little. Forget the amplitudes for a moment. You have two functions which will give you the same magnitude of an answer, with different signs. This is sorta like absolute value. Think of some examples: -1 and 1. -2 and 2. -10 and 10. Notice that the HIGHER THE AMPLITUDE, the GREATER the distance between the two. If you added any of these pairs you would get 0. But if you added DOUBLE the positive one to the negative one, your answer would be the positive number (for example 2 and -2 would be 4 + -2 which is 2, which was the original positive number. With 10 and -10 you'd get 20 + -10 which is 10, which was the original positive number.) That means the higher the magnitude, the greater your answer will be.

Taking that into this problem, you'd want to choose the highest possible value of sin(x) which is 1. Since you want the sin function with the 2 amplitude to be positive, you need to come up with x such that sin(pi + x) = 1. But who cares since it wants the maximum of the entire thing (FYI it would be x = 3pi/2 to name one possibility). You KNOW that you'll get 2 for the value of 2sin(pi + x) and you KNOW that you'll get -1 for the value of sin(x). Since the 2 at the end remains constant, you have 2 - 1 + 2 = 3 which is the max value of this expression.

It makes alot of sense now and quicker too. Thanks again math King! You're like the Neo of Math Matrix. You can see it so fast.