Question 644157: Hello! i got different answer please help!!
Let g be the function defined by g(x) = 10 sin(20x)+30. the maximum value of g is attained at which of the following value of x ?
a. π/2
b. π/10
c. π/20
d. π/30
e. π/40
I think d.is correct answer
since sin (20. π/30) > sin (20.π/40) so it maximize the g(x)
but the answer key said e. is correct answer
please help me verify these.Maybe i am wrong
Thank you in advance!
Found 2 solutions by lwsshak3, DrBeeee:
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Let g be the function defined by g(x) = 10 sin(20x)+30. the maximum value of g is attained at which of the following value of x ?
**
Equation for sin function: Asin(Bx-C), A=amplitude, Period=2π/B, Phase shift=C/B
For given problem we only need to be concerned with the period of the given sin function:
g(x) = 10 sin(20x)+30
B=20
Period=2π/B=2π/20=π/10
As with the sin function, the maximum amplitude occurs at (1/4) of the period.
(1/4) period of given function=π/40 (answer e.)
Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! Your logic for selecting the answer has no bearing on the solution. Firstly, the given choices have nothing to do with each other (true in any MC question) and secondly don't even look at the choices until you solve the problem!
Ask youself,"What is the largest magnitude of the sine (or cosine) function?" The answer is one (1). No matter what angle you pick the absolute value of sin of that angle will never be greater than one. With this in mind look at
(1) g(x) = 10*sin(20x) + 30
This largest this can be is when sin(20x) = +1, then g(x) = 40, but the value of g(x) is not important here. What is important is, "What must 20x be in order that sin(20x) = 1.
Can you tell me, at what angle in radians, does the sine of that angle equals one? I know that the sin(0) = zero, so that's not it. How about 45 degrees (pi/4)? Use your calculator. How about 90 degrees? Voila.
(2) sin(90 degrees) = 1
Then
(3) sin(pi/2) = 1
Your answer is that g(x) is a maximum when
(4) 20x = pi/2 or
(5) x = pi/40
Answer: choice e
You may not want to stop here, but try all the other choices, using your calculator to see if any other give sin(20x) = 1 or g(x) >= 40
For example, choice a) is x = pi/2 or 20x = 10pi which is the same as zero degrees, and sin(0) = 0, giving g(pi/2) = 30 < 40, therefore not the answer.
Likewise b) and c) have sin(20x) = zero. Choice d) has sin(120 degrees) < 1, so is also not the answer. Be careful using your calculator, we usually set them to work in degrees, so if you use pi switch to radians.
Good luck in the future. Beware multiple choice questions! They are evil, and not a guessing game.
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