Thread: Sine function problem

Here's a problem that I have to do for my pre-cal class:
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An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ pi, where x is expressed in radians.

Solve algebraically for all values of x in the interval 0 ≤ x ≤ pi, where the height of the opening, f(x), is 6. Express your answer in terms of pi.

If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?
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I thought I should set f(x) to 6 and solve the equation, which I did, and I got 30 as my answer. But that doesn't make sense because the answer is supposed to expressed in terms of pi, and is supposed to be less than pi. I don't know how else to solve this problem, if anyone could help that would be great! Thanks

degrees to radians ...



don't forget that there is another angle where in quad II

Originally Posted by francesgw

Here's a problem that I have to do for my pre-cal class:
----------------
An architect is using a computer program to design the entrance of a railroad tunnel. The outline of the opening is modeled by the function f(x) = 8 sin x + 2, in the interval 0 ≤ x ≤ pi, where x is expressed in radians.

Solve algebraically for all values of x in the interval 0 ≤ x ≤ pi, where the height of the opening, f(x), is 6. Express your answer in terms of pi.

If the x-axis represents the base of the tunnel, what is the maximum height of the entrance of the tunnel?
----------------

I thought I should set f(x) to 6 and solve the equation, which I did, and I got 30 as my answer. But that doesn't make sense because the answer is supposed to expressed in terms of pi, and is supposed to be less than pi. I don't know how else to solve this problem, if anyone could help that would be great! Thanks

Think pi-radians and not degrees Ya - what skeeter said!

Ohhhh! Hahahah. I can't believe I forgot about converting to radians.. this problem was from a review sheet and I haven't done this type of math in a while. I'm glad I reviewed it! Thanks guys

oh wait! what about the second part of the problem, how to find the maximum height of the tunnel? If the function was just 8 sin x then I think it would be 8, but since it's 8 sin x + 2 I'm not sure where the 2 figures in. Would that make it 10? Or I could be completely off. How do you find the max. height of the tunnel?

what is the max value that sinx can be?

ahhh i don't know! I don't know whether it's in degrees or radians or what.. I mean the max value of a graph of sinx would be 1.. but i don't think that's the answer you're looking for.

okay the max value of sinx is one. So if we plug that into the equation, 8 sinx +2: 8*1+2= 10. Is the maximum 10?

yes ... the max is 10.

8?

I haven't done pre-calc in a while, but if the max value of is 1 then the max can be is 1, .

Originally Posted by OnMyWayToBeAMathProffesor

8?

I haven't done pre-calc in a while, but if the max value of is 1 then the max can be is 1, .

the expression is 8sinx + 2

Edit: Sorry, you already said this. Nevermind.
ok, the maximum value of sin(x) is one. So if we plug that into the equation,

I am sorry, i thought the equation was not . so 10 then?